CTW: From Within Host Dynamics to the Epidemiology of Infectious Disease

(April 7,2014 - April 11,2014 )

Organizers


Steve Cantrell
Mathematics, University of Miami
Mary Galinski
Medicine, Emory University School of Medicine, Division of Infectious Diseases
Juan Gutierrez
Mathematics, Institute of Bioinformatics, University of Georgia

With the advent of genomics, we have learned that microdiversity among strains of the vast majority of pathogens is extensive; each genotype infecting a host can present significant differences in virulence, immunogenicity, and antigenic variation. Thus, pathogens in circulation are not uniform; instead, they are comprised of sub-groups that can be defined by the expression of different genetic, pathogenic and population dynamic traits. The circulation of these parasites depends heavily on human movement dynamics, and, in some situations, vector availability and competence. Together, these anthropological, ecological, molecular, and immunological factors are fundamental drivers in the transmission of infectious disease, and their correct characterization requires a comprehensive interdisciplinary multi-scale modeling approach. This workshop will bring together scientists from multiple disciplines to exchange ideas about new perspectives for the quantification of within-host dynamics and between-host transmission of infectious disease. Attendants will discuss novel molecular and ecological data that has become available at an unprecedented level of detail ('omic, clinical, entomological, and epidemiological data), and will discuss the application of mathematical perspectives that go beyond traditional epidemiological models of transmission.

Accepted Speakers

Linda Allen
Department of Mathematics and Statistics, Texas Tech University
Yael Artzy-Randrup
Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam
John Barnwell
Division of Parasitic Diseases & Malaria, Centers for Disease Control & Prevention
Marcia Castro
Global Health and Population, Harvard School of Public Health
Chris Cosner
Mathematics, University of Miami
Marisa Eisenberg
Department of Epidemiology, University of Michigan
Önder Ergönül
Infectious Diseases, Koc University
Zhilan Feng
Mathematics, Purdue University
Luis Fonseca
The Wallace H. Coulter Department of Biomedical Engineering, Georgia Tech and Emory University
Holly Gaff
Department of Biological Sciences, Old Dominion University
Andreas Handel
Epidemiology & Biostatistics, University of Georgia
Alan Hastings
Department of Environmental Science and Policy, University of California, Davis
Robert Holt
Zoology, University of Florida
Rosalind Howes
Department of Zoology, University of Oxford
Paul Hurtado
Mathematical Biosciences Institute & Aquatic Ecology Laboratory, The Ohio State University
Kevin Lee
Biology, Georgia Institute of Technology
Mark Lewis
Canada Research Chair in Mathematical Biology, University of Alberta
Song Liang
Department of Environmental & Global Health, and Emerging Pathogens Institute, University of Florida
Ivo Müeller
Infection & Immunity, Walter + Eliza Hall Institute
Eric Numfor
Mathematics, University of Tennessee
Sergei Pilyugin
Department of Mathematics, University of Florida
Igor Rouzine
GIVI, Weinberger Lab, The Gladstone Institutes
Shigui Ruan
Department of Mathematics, University of Miami
Mark Styczynski
School of Chemical & Biomolecular Engineering, Georgia Institute of Technology
Joe Tien
Department of Mathematics, The Ohio State University
Rabindra Tirouvanziam
Pediatrics, Emory University
Pauline van den Driessche
Mathematics and Statistics, University of Victoria
Eberhard Voit
Dept. of Biomedical Engineering, Georgia Tech and Emory University
Yanyu Xiao
Department of mathematics, University of Miami
Monday, April 7, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:15 AM

Greetings and Info from MBI - Marty Golubitsky

09:15 AM
09:30 AM

Logistics of the Meeting/Organizers

09:30 AM
10:00 AM
Eberhard Voit - Scientific Overview and Challenges

With this presentation I will try to set the stage for the modeling efforts to be discussed in the workshop. As the title €œFrom Within Host Dynamics to the Epidemiology of Infectious Disease€? directly suggests, infectious diseases involve many scales, with respect to time, space, and organization, with the latter spanning the range from molecules to global effects. While a hallmark goal of systems biology is the integration of heterogeneous information across multiple scales and levels, our computational modeling capabilities are clearly not quite ready to cover all aspects of infectious diseases. Thus, the workshop is hoped to address three fundamental questions, namely:


1. How can modeling help us bridge the gaps between scales or levels of organization?


2. How can we make optimal use of very diverse data (from traditional biology and biochemistry, high-throughput €“omics methods, physiology, clinical observations, host-parasite interactions, disease spread, interventions) in order to deepen our understanding of disease dynamics and adaptation, by both hosts and parasites, and to devise treatment options that are generic or even personalized, and executable at a global scale?


3. What can modelers of different sub-disciplines within the span between within-host-dynamics and epidemiology learn from each other?


In addition to these research questions, the workshop is hoped to discuss means of €œbidirectional€? education between the often separate groups of clinicians and experimentalists on one side and computational analysts on the other. This education should give clinicians and experimentalists a feel for what is achievable with modern modeling tools and help modelers frame specific and relevant biological questions for analyses that offer genuine added value.


As this meeting of expert minds is a workshop rather than a conference, polished answers are not necessarily the goal. Instead, the workshop will be a success if the participants collectively take account of where we are, what we can do with today€™s methods, where we want to be in N years, and what we need to do to get there.



10:00 AM
10:30 AM
Sergei Pilyugin - Deterministic within-host viral dynamics

In this talk, I will review the basic features of deterministic models of within-host viral dynamics. I will discuss the global asymptotic behavior of such models, and extensions of the stability results to models including multi-strain competition, antiviral treatment, and immune response.


10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Zhilan Feng - A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease

A new model is developed for linking the within- and between-host dynamics. The model is motivated by studying the disease dynamics of Toxoplasma gondii, in which the parasite€™s life cycle includes interactions with the environment. We postulate the infection process to depend on the size of the infective inoculum that susceptible hosts may acquire by interacting with a contaminated environment. Because the dynamical processes of the within- and between-host systems occur on different time scales, the model behaviors can be analyzed by using a singular perturbation argument. We define new reproductive numbers for the within-host and between host dynamics for both the isolated systems and the coupled system. Particularly, the reproduction number for the between-host (slow) system dependent on the parameters associated with the within-host (fast) system in a very natural way. We show that these reproduction numbers determine the stability of the infection-free and the endemic equilibrium points. The model is capable of generating a backward bifurcation.

11:30 AM
12:00 PM
Eric Numfor - Optimal Control and Analysis of a Coupled ODE/PDE Immuno-epidemiological Model.

Optimal control can be used to design intervention strategies for the management of infectious diseases, and has been applied in immunological and epidemiological models separately. We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE. Existence and uniqueness of solution to the between-host model is established, and an explicit expression for the basic reproduction number of the between-host model is derived. Stability of disease-free and endemic equilibria of the between-host model is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed. Numerical simulations based on the forward-backward sweep method are obtained.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Robert Holt - Reflections on predation, resources, and the linking of within-host pathogen dynamics to epidemiological processes

Pathogens in a population of hosts in effect live, and dispersing among, habitat €˜patches€™ (viz., individual hosts), with the twist that the patches have their own dynamics, which in turn can be perturbed by the pathogens. Population dynamics in patchy environments quite generally is governed by the interplay of local within-patch conditions (such as resource supply) and coupling via dispersal among patches. Dispersal is a two-edged sword €“ emigration from occupied patches is required to colonize empty patches, but drains individuals from occupied patches, potentially lowering population size there. In this talk I will reflect on comparable processes that may arise in host-pathogen systems. First, I will argue that a consideration of host density-dependence and resource availability can alter expectations about how predation modulates infectious disease prevalence. A laboratory study of viral dynamics in host cell culture will provide an empirical illustration. Second, I will explore epidemiological models which include analogues of emigration (permitting transmission among hosts) impacting within-host pathogen dynamics.

02:30 PM
03:00 PM
Yanyu Xiao - Mathematical model on Malaria with multiple strains of pathogens

Vector-borne diseases are usually associated with infections caused by multiple strains (genotypes) of pathogens. For example, there are several strains of malaria protozoa spreading in different regions. Globalization and modern transportation raise a natural concern of possible epidemics caused by multiple strains of parasites in one region. In this study, we use mathematical models to explore such a possibility. Firstly, we propose a model to govern the within-host dynamics of two strains. Analysis of this model practically excludes the possibility of co-persistence (or super-infection) of the two strains in one host. Then we move on to set up another model to describe the dynamics of disease transmission between human and mosquito populations without the co-infection class (using the results for the within-host model). By analyzing this model, we find that co-endemic caused by both strains in a single region are possible within certain range of model parameters. This is a joint work with Xingfu Zou.

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Linda Allen - Thresholds for Extinction in Stochastic Models of Infectious Diseases: Importance of Time and Location

Relations between Markov chain models and differential equation models for infectious diseases near the infection-free state are derived. Approximation of the Markov chain model by a multitype branching process leads to an estimate of the probability of disease extinction. We summarize some extinction results for multi-patch, multi-group, and multi-stage models of infectious diseases for epidemics and within-host models. The successful invasion of a pathogen often depends on the conditions of the environment at a specific time and location.


04:00 PM
04:30 PM

Discussion

04:30 PM
06:30 PM

Reception and Poster Session in MBI Lounge

06:30 PM

Shuttle pick-up from MBI

Tuesday, April 8, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Joe Tien - Disease invasion of community networks with environmental pathogen movement

Consider a set of communities (patches), connected to one another by a network. When can disease invade this network? Intuitively, this should depend upon both the properties of the communities, as well as on the network structure. Here we make this dependence explicit for a broad class of disease models with environmental pathogen movement. In particular, the rooted spanning trees of the network and a generalization of the group inverse of the graph Laplacian play fundamental roles in determining the ability of disease to invade. This is joint work with Z. Shuai, M. Eisenberg, and P. van den Driessche.

09:30 AM
10:00 AM
Marisa Eisenberg - Identifiability and interacting scales in modeling disease dynamics

Disease processes often involve interacting factors at multiple scales, which can affect both how we build models of these systems and the data sets needed to estimate model parameters. In this talk I will discuss some examples of disease transmission models that depend on processes at scales ranging from cellular to environmental, including cholera and human papillomavirus (HPV).

10:00 AM
10:30 AM

Discussion

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Paul Hurtado - Within-host to population-level modeling of mycoplasmal conjunctivitis in wild birds

The pathogenic bacterium Mycoplasma gallisepticum jumped from poultry into North American House Finch populations during the early 1990s, and has since proven to be an accessible system in which to study the many faces of emerging infectious diseases in vertebrates. In this talk I'll begin by introducing the system, then I'll discuss some sources of individual-level variation in this system (and likely many others) including some results obtained by "scaling up" from the individual level. Then, I'll discuss the use of models to address questions at the population level including evolutionary dynamics and the importance of a novel virulence trade-off present in this system which is likely a factor driving evolutionary dynamics of other parasites with mobile host species.

11:30 AM
12:00 PM
Pauline van den Driessche - Coexistence or Replacement of two Subtypes of Influenza

From observations, a pandemic subtype of influenza A sometimes replaces but sometimes coexists with the previous seasonal subtype. For example, the 1957 pandemic subtype H2N2 replaced the seasonal subtype H1N1; whereas after 1977 subtypes H1N1 (from the pandemic) and H3N2 continue to coexist. In an attempt to understand these alternatives, a model for the dynamics of influenza during an epidemic season is formulated taking into account cross immunity depending on the most recent seasonal infection. This cross immunity is assumed to reduce susceptibility to related strains of the seasonal subtype, and to wane with time due to virus drift. The population reaches an equilibrium distribution in susceptibility after several seasons, and then a pandemic subtype appears to which individuals in the population all have the same cross immunity. Threshold conditions for coexistence or replacement are derived from the model, with the conditions depending on the reproduction number of seasonal influenza and the level of cross immunity between the seasonal and pandemic subtypes. This is a preliminary report on joint work with S.M. Asaduzzaman and J. Ma.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Song Liang - Transmission of Cholera in the Far North Region of Cameroon - A Model-Guided Exploration

Cholera was first reported in West Africa in early 1970s and became endemic in the region since then. In 2010, one of major cholera epidemics occurred in West Africa and in the Lake Chad area (covering Cameroon, Nigeria, Chad, and Niger) more than 57,000 reported cases and 2,466 deaths were reported. In the Far North Region of Cameroon, the worst-hit region in the Lake Chad area, more than 9,400 cases and 600 deaths were reported. Yet, little is known on how the disease was transmitted and spread in the region. In this study, we first explore temporal patterns of cholera outbreaks and their associations with environmental factors (e.g. rainfall and temperature) based on 15-year€™s (1996 €“ 2011) cholera cases reported weekly in the Far North Region. A wavelet approach is used to account for noisy and non-stationary nature of the cholera outbreak data and possibly transient relationships between cholera transmission and environmental factors. We then explore possible transmission mechanisms underlying the 2010 major cholera outbreak in the Far North using a mathematical model. Through extending the classic susceptible-infected-recovered (SIR) framework, we develop a meta-community model to assess how socio-environmental factors, in particular rainfall and human movement, might contribute to the cholera transmission in the Far North Region. The analyses have offered some important insights into drivers associated with the cholera transmission in the region and, guided by the modeling explorations, we have proposed some priorities for field epidemiological and environmental studies on ground.


02:30 PM
03:00 PM
Holly Gaff - Epidemiology of tick-borne Rickettsia spp.

The incidence of tick-borne rickettsial disease in the southeastern United States has been rising steadily through the past decade, and the range expansions of tick species and tick-borne infectious agents, new and old, has resulted in an unprecedented mix of vectors and pathogens. The results of an ongoing 5-year surveillance project describe the relative abundance of questing tick populations in southeastern Virginia. Since 2009, more than 100,000 questing ticks of a variety of species have been collected from vegetation in a variety of habitats, with Amblyomma americanum constituting over 95% of ticks collected. We found that 26.9€“54.9% of A. americanum ticks tested were positive for Rickettsia amblyommii, a non-pathogenic symbiont of this tick species. Rickettsia parkeri was found in 41.8€“55.7% of Amblyomma maculatum ticks. The rate of R. parkeri in A. maculatum ticks is among the highest in the literature and has increased in the 2 years since R. parkeri and A. maculatum were first reported in southeastern Virginia. Additionally, R. parkeri is started to be found in A. americanum ticks throughout the region. While this is at extremely low prevalence, the sheer abundance of these ticks may increase the encounters with rickettsial agents with the potential for increased risk to human health.

03:00 PM
03:30 PM

Discussion

03:30 PM
04:00 PM

Break

04:00 PM
04:30 PM
Önder Ergönül - Crimean-Congo Hemorrhagic Fever: Why Do We Need a Model?

Crimean-Congo hemorrhagic fever (CCHF) is a fatal viral infection described from Africa, Asia, Southeastern Europe, and the Middle East1. The CCHF virus (CCHFV) belongs to the genus Nairovirus in the family Bunyaviridae, and causes severe disease in humans, with a reported case fatality rate of 3-30%. Humans can become infected through the bites of ticks, by contact with patients' body fluids, or by contact with blood or tissues from viremic livestock. Some occupational groups, including health care workers (HCW) are under risk of CCHF infection. Health care related CCHF infections were reported in Pakistan, United Arabic Emirates, South Africa, Iran, India, Tajikistan and Turkey. The greatest risk factor, however, is working with animals. The tick attaches itself to cattle, sheep, and goats. Around 30 countries in Africa, Asia, and Europe have reported CCHF. The tick ventures no further than 50° north latitude, which cuts across Russia, the Ukraine, and central Europe and France; the latter two regions are not considered to be at any immediate risk, the vector is present but there is no serological evidence of CCHF.



As with all vector-borne diseases, several ecological and anthropocentric factors are likely to affect the disease€™s occurrence: increases in bush-type habitats, for example, and increases in wild animal populations or decreases in domestic animal populations. The first documented outbreak is a case in point. CCHF was initially recognized in 1944. USSR forces had driven the Germans out of the Crimea. During the occupation, farming activities had fallen into abeyance. People stopped hunting hares, and pastures became overgrown. When the Soviets recovered the Crimea, its soldiers, new settlers to the region, began to fall sick. (In 1969, the same virus was found to be responsible for a 1956 outbreak in the Congo, hence the name).



Changing patterns of agriculture and flood controls may also have played a part. In the Soviet Union, agriculture was collectivised and flood plains converted to farmland. Affected parts of central Anatolia had been more or less abandoned in the late 1990s due to terrorist activity. Hunting and farming resumed in 2001, and ticks were able to fasten upon the influx of cattle and sheep. The following year, Turkey confirmed its first case of CCHF and numbers have steadily increased ever since.



There are at least four reasons why we might want to use mathematical models to study CCHF.



1.Modeling can help us to gain a qualitative understanding of the dynamics of the disease and, in this way, help us to improve our intuition.



2.Second, by highlighting key uncertainties and gaps in our knowledge models may suggest observational or experimental studies that would improve our understanding of key aspects of the whole system. This is likely to be particular important in the area of understanding the vector dynamics where major uncertainties exist for CCHF. Since models can also be considered to be hypotheses about the systems, by confronting models with data we can effectively choose between competing hypotheses.



3.Third, models can help in the selection and evaluation of control policies. This can be done by employing models as statistical tools used to estimate the effect of interventions that have been made (and, equally importantly, to quantify the uncertainty in these estimates). Having quantified the effect of individual interventions, we can then go on to use models to ask €œwhat-if€? questions, using models predictively to determine the expected effect of hypothetical combinations of interventions. More generally, by enabling us to identify the most critical parameters affecting the behavior of the system, models can help us in setting priorities and identifying the most cost-effective control policies. Indeed, the use of dynamic models is essential for accurate economic analyses of control measures for infectious diseases.



4.Fourth, there is the potential to use models for forecasting the future of epidemics. Though popularly imagined as one of the main uses of models (perhaps by analogy to the models used to derive weather forecasts) this is one of the least developed areas in the infectious disease modeling literature, although there is increasing interest in this application.



One of the most useful concepts in infectious disease epidemiology is the case reproduction number: the average number of secondary cases caused by a primary case. For a tick-borne disease, we can define R0 as the average number of secondary infections in hosts from one primary infected host (when all hosts and ticks are susceptible) or, equivalently, as the average number of infectious ticks that arise from a single infected tick in a susceptible population. A simple SEIR modeling framework could be illustrated.



In many cases it is useful to estimate R0. The estimate will tell us how close we are to a risking a major epidemic (if R0 is currently below one) and allow precautionary measure to be taken. If R0 is greater than one the estimate tells us how much an intervention would have to do to bring about control or eliminate the chance of a major epidemic. An approach that has proved useful for other diseases is to estimate R0 from the distribution of the number of cases from clusters of transmission.



When more detailed surveillance data are available other approaches can be used to provide much better estimates of R0 and to assess the impact of interventions.



04:30 PM
05:00 PM

Discussion

05:00 PM

Shuttle pick-up from MBI

Wednesday, April 9, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
John Barnwell - Within-Host and Between-Host Determinants of the Biology of Malaria Infections

Human malaria is actually a complex of mosquito-borne parasite infections with intricate lifecycles that manifest as a diverse group of diseases within and between the causative species. This disease complexity is influenced by various within and between host factors such as the biology of the different Plasmodium species, the innate and adaptive responses of the human host, and the biology of the mosquito hosts. A number of robust nonhuman primate models that represent the diversity of human malaria disease exist and allow study in a more controlled environment. This talk will discuss some of these factors and how they might influence human disease presentation, transmission, and epidemiological and within host dynamics.

09:30 AM
10:00 AM
Yael Artzy-Randrup - Synergistic and antagonistic interactions between bed-nets and vaccines in the control of malaria

The nature by which immunity is gained is known to play an important role in shaping population level epidemiological patterns. Here we address the general consensus that integrating different malaria intervention approaches will always act synergistically for malaria control. Using a fully parameterized mathematical model to investigate the interaction of treated bed-nets with vaccination in the population dynamics of malaria, we demonstrate that mixed interventions create non-linear responses that modify the way in which human hosts acquire protection against future malaria infection. Our results indicate that vaccines will not necessarily provide a straightforward solution to malaria control, and that future programs need to consider both synergistic and antagonistic interactions between vaccines and other control measures.

10:00 AM
10:30 AM

Discussion

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Mary Galinski - The Malaria Host-Pathogen Interaction Center: a Systems Biology Coalition

The Malaria Host-Pathogen Interaction Center is led by investigators from Emory University, the University of Georgia (UGA), the Georgia Institute of Technology (GA Tech), and the Centers for Disease Control and Prevention (CDC), and includes collaborators from around the world. The project involves the longitudinal analysis of malaria infections in several non-human primate (NHP) models using high throughput technologies including immune profiling, functional genomics, proteomics, lipidomics, and metabolomics to generate data on host-pathogen interactions and an improved understanding of pathogenesis. In addition, the MaHPIC aims to develop metabolomic profiles from cross-sectional samples of human malaria infections from geographically diverse malaria endemic countries with a variety of epidemiological settings, and also consider broader systems based studies through such collaborations. The team is developing mathematical models of the parasite and host dynamics, as well as their interactions, to develop approaches to the prediction of various malarial clinical outcomes. Datasets will be deposited into a repository system that will feed a relational database (e.g., MaHPIC-DB) making the data accessible for bioinformatics, modeling and ongoing analysis and deeper investigation by the broad research community.

11:30 AM
12:00 PM
Kevin Lee - Functional genomics of Malaria host-pathogen interaction center

The functional genomics core of the Malaria Host-Pathogen Interaction Center (MaHPIC) is using RNA-Seq to jointly profile gene expression in host non-human primate and Plasmodium parasite transcriptomes from peripheral blood samples during an infection cycle. I will report results from the first experiment, a modeling of relapsing malaria involving the macaque and P. cynomolgi, where we have seven time points from four individual macaques. As well as documenting among-individual variability and responses that cycle during phases of relapse, I will report on analytical methods leading toward integration of diverse types of omic data, principally transcriptomic, metabolomic, lipidomic, and immunological.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Mark Styczynski - Systems-scale and integrative "omic" analysis of host-pathogen interactions in malaria

As part of the Malaria Host-Pathogen Interaction Center, our goal is to study and model the response of both host and pathogen to the course of malarial infection, treatment, and recurrence or recrudescence, using multiple levels of "omic" data. Detailed mathematical models are a desired ultimate product of our study of malaria, and while there are certainly some intuitive candidate systems for such modeling, it is not necessarily clear a priori which other systems should be modeled, nor which variables are important to include in those models. Our goal is to exploit the multiple levels of systems-scale datasets being generated in our center to identify such candidates for detailed models and follow-up experiments.


The main task in achieving this goal is discovery of novel, unknown interactions between our measured variables. This can be accomplished via a number of classes of approaches, including statistical analyses and machine learning. Here, we will focus on our machine learning approaches to identifying subnetworks of interesting interactions, specifically using probabilistic graphical models to construct interaction networks. Within this domain, two of the biggest obstacles to accomplishing our goal are 1) computational tractability given the high dimensional variable space, and 2) integrating multiple disparate data types, each with potentially different scales of variable space dimensionality (tens of measurements vs. tens of thousands of measurements) and different time scales, such that no data type dominates or is dwarfed in importance. We will present our algorithmic work addressing these problems, along with applications to the malaria data that has been generated by our center to date.


02:30 PM
03:00 PM
Luis Fonseca - Modeling The Blood Stage Infection In Malaria: Advantages Of Discrete Versus Continuous Approaches

The blood stage of a malaria infection is the final step of the dual-host multi-stage disease. It is at this stage that most symptoms manifest and where the outcome is critical for the future disease trajectory toward either chronic infection or death. The blood stage is marked by the interplay between malarial merozoites, the erythropoietic system, and the immune system. Failure to properly up-regulate erythropoiesis results in anemia, while an improper immune response may lead to chronic infection that is characterized by recrudescence or relapse.


The production of red blood cells (RBCs) by the erythropoietic system takes about 5 days in our model organism, Macaca mulatta, and the RBCs normally remain in the blood stream for about 100 days. During this life cycle, only RBCs of the early age-classes are prone to merozoite invasion. Upon invasion, growth of the tropozoites into schizonts and the subsequent release of about 14 to 20 new merozoites take about 48 hours for the infecting parasite, Plasmodium cynomolgi. A computational systems analysis of the processes involved in the dynamics of RBCs in malaria demonstrated that the blood stage events are strongly dependent on different time delays and the structure of age-classes among the RBCs.


In this workshop presentation, we will discuss the advantages and disadvantages of using: ordinary differential equation (ODE) models with and without age-classes; delay differential equations (DDE); or discrete recursive models with age-classes. DDEs and ODEs with age-classes are well suited for the generation of delays, but lack the required flexibility to properly address issues associated with the constantly changing differentiation time of RBC precursors. By contrast, discrete recursive models allow the proper movement of all cells through their life cycle, while also allowing variables to be associated with dynamically changing delays, amplification ratios, and different types of injuries or infections, including malaria.


03:00 PM
03:30 PM

Discussion

03:30 PM
04:00 PM

Break

04:00 PM
04:30 PM
Rosalind Howes - Insights into Plasmodium vivax from spatial maps of human gene polymorphisms: Duffy blood group and G6PD deficiency.

Over a third of the world€™s population lives at risk of potentially life-threatening Plasmodium vivax malaria infections. Unique aspects of this parasite€™s biology and interactions with its human host make it harder to control and eliminate than the better studied Plasmodium falciparum parasite. The spatial epidemiology of two human genetic systems associated with these traits has been investigated in a multi-scale, model-based framework to generate estimates of populations of risk of P. vivax infection, and assessments of associated therapeutic risks.


First, the two key SNPs determining expression of the Duffy blood group were modelled to map the prevalence of Duffy phenotypes globally. The Duffy antigen is the only known erythrocyte receptor for P. vivax infection, and was used as a proxy indicator of population susceptibility to infection. The maps are discussed in light of reports of apparent Duffy-independent transmission.


Second, the global epidemiology of G6PD enzyme deficiency €“ both its phenotypic prevalence and genetic heterogeneity €“ is mapped. A geostatistical framework structured around the gene€™s X-linked inheritance generated global estimates of G6PD deficiency prevalence, and estimates of affected population numbers. Poorly quantified risks from this spatially heterogeneous enzyme deficiency currently hinder widespread use of primaquine, a drug necessary for progress towards malaria elimination, particularly against the relapsing P. vivax life-stages.


These examples illustrate the positive contribution that integrating spatial epidemiological human genetic data can make in supporting the evidence-base for strategic planning for control of an infectious disease, thereby attempting to bridge the gap between basic biological research and the health sciences.


04:30 PM
05:00 PM

Discussion

05:00 PM

Shuttle pick-up from MBI

05:00 PM
06:00 PM

Cash Bar

06:00 PM
08:00 PM

Banquet in the Fusion Room at Crowne Plaza

Thursday, April 10, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Marcia Castro - Spatial and Temporal Malaria Risk Profiles

The modern era of Amazon frontier expansion in Brazil witnessed the introduction of large-scale colonization projects focused on agriculture and wide-ranging human settlement, as well as the construction of infrastructure, such as roads and dams. These initiatives led to massive human migration, substantial environmental transformation, and severe malaria transmission. Interactions between development efforts, agricultural colonization, environment and health, at given levels of socioeconomic conditions, are very complex and demand a multidisciplinary analysis to serve as the basis for rational and successful policies. The talk will focus on a specific settlement project, and present a spatially explicit methodological approach that combined spatial analysis, geostatistical tools, and fuzzy sets, in a multidisciplinary way, in order to identify the most important factors impacting transmission. Results revealed that during the early stages of frontier settlement transmission was mainly driven by environmental risks, consequential to ecosystem transformations that promote larval habitats of Anopheles darlingi. With the advance of forest clearance and the establishment of agriculture, ranching, and urban development, malaria transmission was substantially reduced, and risks of new infection were largely driven by human behavioral factors.

09:30 AM
10:00 AM
Rabindra Tirouvanziam - Tracking dynamic innate immune responses in experimental malaria infection

Experimental malaria infections in non-human primates (NHPs) are a prime setting to assess the changing biological conditions associated with disease, notably with regards to the host immune system. While much attention has been focused on T-cell and B-cell dependent ("adaptive") responses that are key to vaccine development and long-term protection in malaria, relatively little is known of the involvement of the innate immune system. Here, we will highlight a novel approach that addresses this gap in knowledge, and will show early data obtained as part of the Malaria Host Pathogen Interaction Center (MaHPIC) consortium at Emory University, Georgia Tech and University of Georgia (PI: Mary Galinski, Co-PIs: Alberto Moreno, Jessica Kissinger). By tracking functional responses mounted by the innate immune system in malaria-infected NHPs, we show that this arm of the immune system is mobilized to a major extent during the course of infection. This data is the first of its kind and will be discussed in relation to integration with other omics technologies and use in building mathematical models that include both adaptive and innate host immunity.


Chet Joyner, Mary Galinski, Rabindra Tirouvanziam, Emory University

10:00 AM
10:30 AM

Discussion

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Chris Cosner - Some effects of host movement in vector-borne disease systems

Host movements can have a profound impact on the transmission of vector-borne diseases because they can increase or reduce he rate of contact between hosts and vectors. It is clear that host movement can introduce pathogens to new environments, but models suggest that it can also increase or decrease the basic reproduction number (R0) within an environment by influencing the contact rates between hosts and infected vectors or between vectors and infected hosts. There are two distinct types of movement that are relevant in this context. They can be characterized as commuting and migration. The distinction is that migration envisions hosts changing the location of their primary residence, while commuting envisions that each host maintains a particular location of residence but visits other locations in the course of routine activities. These two types of movement require different models and may have different effects. This talk will review some models and results for the effects of host movement in vector-borne disease systems.


11:30 AM
12:00 PM
Andreas Handel - Flu in ducks and water - a multiscale modeling study

It has recently been suggested that for avian influenza viruses, prolonged persistence in the environment plays an important role in the transmission between birds. In such situations, influenza virus strains may face a trade-off: They need to persist well in the environment at low temperatures, but they also need to do well inside an infected bird at higher temperatures. Here, we report an analysis of fitness for avian influenza A viruses across scales, focusing on the phenotype of viral persistence. Taking advantage of a unique dataset that not only reports environmental virus persistence, but also strain-specific viral kinetics from duck challenge experiments, we show that the environmental persistence phenotype of a strain does not impact within-host infection dynamics and virus load. We thereby establish that for this phenotype, the scales of within-host infection dynamics and between-host environmental persistence do not interact: the virus can optimize fitness on each scale without cross-scale trade-offs. Instead, we confirm the existence of a temperature-dependent persistence trade-off on a single scale, with some strains optimizing environmental persistence in water at low temperatures while others reduce sensitivity to increasing temperatures.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Mark Lewis - Ecological dynamics of a salmon parasite

In this talk I will outline the impact that parasitic sea lice have on the ecology of pacific salmon and the role that parasite spill over and spill back with aquaculture has taken in modifying the ecology of pacific salmon. These modifications are far reaching, and include changes in salmon returns, establishment of nonlinear population thresholds such as Allee effects, and shifts in predator prey dynamics. My talk will involve a mixture of modelling and data, based on over a decade of intensive field work.

02:30 PM
03:00 PM
Shigui Ruan, Chris Cosner - Within Host Dynamics of HIV and Malaria Co-infection

Malaria and HIV are among the most serious global health problems of our time. Together, malaria and HIV/AIDS cause more than 4 million deaths worldwide each year. Co-infection occurs in sub-Saharan Africa because there are wide geographical and epidemiological overlaps. Adverse effects of either infection on the other could have serious implications. In this talk, we propose a mathematical model to study the dynamics of immune responses to both malaria and HIV within a host of co-infection. The goal is to investigate the effect of HIV infection on malaria by studying the blood-stage dynamics of co-infection in individual hosts and incorporating red blood cells, CD4+ T cells, malaria parasitemia, HIV and immune effectors into a mathematical model. Numerical simulations demonstrate that HIV increases the risk of severe clinical malaria infection with higher density of parasitemia and more likely acute fever. (This talk is based on a joint manuscript with Dongmei Xiao).

03:00 PM
03:30 PM

Discussion

03:30 PM
04:00 PM

Break

04:00 PM
04:30 PM
Juan Gutierrez - Systems biology of epidemiology From genes to environment

Traditional epidemiological models consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). These models are challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: Simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus causing individual to belong to multiple compartments simultaneously. (ii) Antigenic diversity and variation: Antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, and antigenic diversity, defined as antigenic differences between pathogens in a population, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission. This talk explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics in environmental transmission. A basic propagation number is calculated that could guide public health policy.

04:30 PM
05:00 PM

Discussion

05:00 PM

Shuttle pick-up from MBI

Friday, April 11, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Alan Hastings - Parallels between metapopulations and disease dynamics

Within host dynamics in diseases is essentially the same as dynamics within metapopulations in an ecological context. I will review results from metapopulation models, and draw parallels to disease dynamics. I will emphasize both similarities and differences. The goal will be to see how various assumptions about within host (equivalently within patch) dynamics reduce the complexity of the model and study and lead to models which can be studied analytically.

09:30 AM
10:00 AM
Igor Rouzine - Interference particles as resistance-proff antiviral therapy: Cost-benefit tradeoff and the evolutionary conflict between two biological scales

A major obstacle to the development of anti-viral therapies is the rapid evolution of viral resistance. HIV models provide a good context for investigation of means for resistance-proofing treatments. A proposed resistance-proof system for HIV therapy involves the use of defective copies of the virus, therapeutic interfering particles (TIPs), which interfere with viral action at a cellular scale by co-opting viral resources in order to further their own spread, but which do not spread in the absence of the virus. This mechanism of action allows for viral suppression not only within a single cell, but also throughout an HIV-infected host, and across a population of hosts. Extending a previously described multiscale model for TIP action, we show that TIPs can invade existing populations of HIV-infected individuals if the initial prevalence of HIV is large enough, and investigate the emergence of resistance within a population after a successful course of TIP intervention. We then show that by adjusting the relative rates of TIP and HIV transcription, we can produce suppression of HIV within a population while simultaneously hampering the spread of TIP resistant mutants and promoting the spread of susceptible ones. In this parameter region, the benefit of resistance and its cost are tightly related, with the cost exceeding the benefit. This stands in contrast to the case of antiviral drugs, where the two are independent and vary over a broad range. We propose experiments in chemostat and nonhuman primate models to test the key aspects of our findings.

10:00 AM
10:30 AM

Discussion

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Ivo Müeller - The molecular epidemiology of P. vivax in Papua New Guinea

In co-endemic areas, the risk of infections and disease with P. vivax decreases more rapidly with age than that of P falciparum, indicating a substantially more rapid acquisition of immunity to infections with P. vivax. By genotyping all PCR-positive infections in a cohort of children it is possible to directly measure the incidence of genetically distinct bloodstone infections (i.e. molecular force of (bloodstone) infections, molFOB). By applying these methods to cohort of children 1-3 years of age, we found that they experience 2.5-times as many genetically distinct P. vivax (molFOB=14.0) than P. falciparum infections (molFOB=5.5) and that children with the highest exposure show fastest decrease decrease incidence of clinical P. vivax episodes. In P. falciparum, where immune acquisition if still limited, children with high exposure have the highest risk of illness. By clearly long-lasting dormant liver stage parasites (i.e. hypnzoites) in 247 of 504 children aged 5-10 year, we were subsequently able to show that relapses from hypnozoites infections account for ~80% of blood stage infections. A comparable proportion of relapses vs. primary infections we found by stochastical modelling of in-host dynamics of P. vivax infections the cohort of children 1-3. This indicated that P. vivax relapses contribute significantly to the higher P. vivax molFOI and more rapid acquisition of immunity.

11:30 AM
12:00 PM

Break/Poster Session Last View

12:00 PM

Shuttle pick-up from MBI (One to Hotel/One to Airport)

Name Affiliation
Allen, Linda linda.j.allen@ttu.edu Department of Mathematics and Statistics, Texas Tech University
Arino, Julien arinoj@cc.umanitoba.ca Mathematics, University of Manitoba
Artzy-Randrup, Yael Yael.Artzy@UvA.nl Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam
Barnwell, John wzb3@cdc.gov Division of Parasitic Diseases & Malaria, Centers for Disease Control & Prevention
Ben-Shachar, Rotem rbenshachar@gmail.com Computational Biology and Bioinformatics, Duke University
Borchering, Rebecca rborchering@ufl.edu Mathematics, University of Florida
Buckalew, Richard rb301008@ohio.edu Mathematics, Ohio University
Capistran, Marcos marcos@cimat.mx Mathematics, CIMAT A.C.
Castro, Marcia mcastro@hsph.harvard.edu Global Health and Population, Harvard School of Public Health
Chen, Jing j.chen@math.miami.edu Mathematics, University of Miami
Chitsa, Gesham gmagombedze@gmail.com NIMBioS, University of Tennessee, NIMBioS
Christen, Andres jac@cimat.mx PyE, Centro de Investigacion en Matematicas (CIMAT)
Coates, Jessica j.l.coates@emory.edu Microbiology and Molecular Genetics, Emory
Cosner, Chris gcc@math.miami.edu Mathematics, University of Miami
Craft, Meggan craft@umn.edu Veterinary Population Medicine, University of Minnesota
Eisenberg, Marisa marisae@umich.edu Department of Epidemiology, University of Michigan
Ergonul, Onder oergonul@ku.edu.tr Infectious Diseases, Koc University
Faraimunashe, Chirove chirovef@ukzn.ac.za School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal
Feng, Zhilan zfeng@math.purdue.edu Mathematics, Purdue University
Fonseca, Luis llfonseca@gatech.edu The Wallace H. Coulter Department of Biomedical Engineering, Georgia Tech and Emory University
Gaff, Holly hgaff@odu.edu Department of Biological Sciences, Old Dominion University
Galinski, Mary mgalins@emory.edu Medicine, Emory University School of Medicine, Division of Infectious Diseases
GAO, DAOZHOU Daozhou.Gao@ucsf.edu Francis I. Proctor Foundation, University of California, San Francisco, Francis I. Proctor Foundation, UCSF
Govinder, Kesh govinder@ukzn.ac.za Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Gutierrez, Juan jgutierr@uga.edu Mathematics, Institute of Bioinformatics, University of Georgia
Hamilton, Ian hamilton.598@osu.edu EEOB/Mathematics, The Ohio State University
Handel, Andreas ahandel@uga.edu Epidemiology & Biostatistics, University of Georgia
Hastings, Alan amhastings@ucdavis.edu Department of Environmental Science and Policy, University of California, Davis
Healy Profitós, Jessica healy.50@osu.edu Division of Environmental Health Sciences, College of Public Health, The Ohio State University
Holt, Robert rdholt@zoo.ufl.edu Zoology, University of Florida
Howes, Rosalind rosalind.howes@zoo.ox.ac.uk Department of Zoology, University of Oxford
Hurtado, Paul hurtado.10@mbi.osu.edu Mathematical Biosciences Institute & Aquatic Ecology Laboratory, The Ohio State University
Jacobs, Nathan nathan.jacobs@emory.edu Biology, Emory University
Jennings, Rachel rfarris4@uwyo.edu Mathematics, University of Wyoming
Jonsson, Colleen cbjons01@louisville.edu Microbiology and Immunology, University of Louisville
Just, Winfried mathjust@gmail.com Department of Mathematics, Ohio University
Kayode, Kolawole mutairu.kolawole@uniosun.edu.ng Dept of Mathematical and Physical Sciences, Osun State University, Osogbo, Nigeria.
Lee, Kevin klee370@gatech.edu Biology, Georgia Institute of Technology
Lelu, Maud lelu@nimbios.org Division of Epidemiology and Community Health, University of Minnesota
Lewis, Mark mlewis@math.ualberta.ca Canada Research Chair in Mathematical Biology, University of Alberta
Liang, Song songliang@ufl.edu Department of Environmental & Global Health, and Emerging Pathogens Institute, University of Florida
Martcheva, Maia maia@math.ufl.edu Mathematics, University of Florida
Mastroberardino, Antonio axm62@psu.edu School of Science, Pennsylvania State University
momoh, abdulfatai itsfaithy@yahoo.com departments pf mathematics, modibbo adama university of technology, yola. nigeria
Mueller, Ivo ivomueller@fastmail.fm Infection & Immunity, Walter + Eliza Hall Institute
Mukherjee, Sayak smukhe04@vt.edu Physics, Virginia Polytechnic Institute and State University
Ngonghala, Calistus cnngonghala@nimbios.org Global Health and Social Medicine, Harvard Medical School
Numfor, Eric numfor@math.utk.edu Mathematics, University of Tennessee
Phepa, Patrick phepa05@gmail.com Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Pilyugin, Sergei pilyugin@math.ufl.edu Department of Mathematics, University of Florida
Pomeroy, Laura pomeroy.26@osu.edu Veterinary Preventive Medicine, Ohio State University
Ponciano Castellanos, Jose josemi@ufl.edu Biology, University of Florida
Rouzine, Igor igor.rouzine@gladstone.ucsf.edu GIVI, Weinberger Lab, The Gladstone Institutes
Ruan, Shigui ruan@math.miami.edu Department of Mathematics, University of Miami
Saenz, Roberto rasaenz@gmail.com Facultad de Ciencias, Universidad de Colima
Salaam, Bolanle bsalaam@uga.edu Mathematics, University of Georgia
Shuai, Zhisheng shuai@ucf.edu Mathematics, University of Central Florida
Styczynski, Mark mark.styczynski@chbe.gatech.edu School of Chemical & Biomolecular Engineering, Georgia Institute of Technology
Tang, Yan yan.tang@biology.gatech.edu Biology, Georgia Institute of Technology
Tien, Joe jtien@math.ohio-state.edu Department of Mathematics, The Ohio State University
Tirouvanziam, Rabindra tirouvanziam@emory.edu Pediatrics, Emory University
TOSUN, KURSAD ktosun@siu.edu Mathematics, Vassar College
Uppal, Karan kuppal2@emory.edu MaHPIC, Emory University
van den Driessche, Pauline pvdd@math.uvic.ca Mathematics and Statistics, University of Victoria
Voit, Eberhard eberhard.voit@bme.gatech.edu Dept. of Biomedical Engineering, Georgia Tech and Emory University
Wang, Jin j3wang@odu.edu Mathematics, Old Dominion University
williams, paul pauldw@princeton.edu Ecology and Evolutionary Biology, Princeton University
Xiao, Yanyu yanyuxiao@gmail.com Department of mathematics, University of Miami
Xue, Chuan cxue@math.osu.edu Department of Mathematics, The Ohio State University
Yan, Paul pypaul@uga.edu IOB, UGA
Yong, Kamuela kamuela.yong@asu.edu Mathematical, Computational and Modeling Sciences Center, Arizona State University
Young, Glenn gsy2@pitt.edu Mathematics, University of Pittsburgh
Zhao, Ruijun ruijun.zhao@gmail.com Department of Mathematics and Statistics, Minnesota State University, Mankato
Thresholds for Extinction in Stochastic Models of Infectious Diseases: Importance of Time and Location

Relations between Markov chain models and differential equation models for infectious diseases near the infection-free state are derived. Approximation of the Markov chain model by a multitype branching process leads to an estimate of the probability of disease extinction. We summarize some extinction results for multi-patch, multi-group, and multi-stage models of infectious diseases for epidemics and within-host models. The successful invasion of a pathogen often depends on the conditions of the environment at a specific time and location.


Synergistic and antagonistic interactions between bed-nets and vaccines in the control of malaria

The nature by which immunity is gained is known to play an important role in shaping population level epidemiological patterns. Here we address the general consensus that integrating different malaria intervention approaches will always act synergistically for malaria control. Using a fully parameterized mathematical model to investigate the interaction of treated bed-nets with vaccination in the population dynamics of malaria, we demonstrate that mixed interventions create non-linear responses that modify the way in which human hosts acquire protection against future malaria infection. Our results indicate that vaccines will not necessarily provide a straightforward solution to malaria control, and that future programs need to consider both synergistic and antagonistic interactions between vaccines and other control measures.

Within-Host and Between-Host Determinants of the Biology of Malaria Infections

Human malaria is actually a complex of mosquito-borne parasite infections with intricate lifecycles that manifest as a diverse group of diseases within and between the causative species. This disease complexity is influenced by various within and between host factors such as the biology of the different Plasmodium species, the innate and adaptive responses of the human host, and the biology of the mosquito hosts. A number of robust nonhuman primate models that represent the diversity of human malaria disease exist and allow study in a more controlled environment. This talk will discuss some of these factors and how they might influence human disease presentation, transmission, and epidemiological and within host dynamics.

An Analysis of the Interaction Between Influenza and Syncytial Respiratory Virus Based on Acute Respiratory Infection Records

Under the hypothesis that both influenza and respiratory syncytial virus (RSV) are the two leading causes of acute respiratory infections (ARI), in this paper use a standard two-pathogen epidemic model as a regressor to explain, on a yearly basis, high season ARI data in terms of the contact rates and initial conditions of the mathematical model.

The rationale is that ARI high season is a transient regime of a noisy system, e.g., the system is driven away from equilibrium every year by fluctuations in variables such as humidity, temperature, viral mutations and human behavior.

Using the value of the replacement number as a phenotypic trait associated to fitness, we provide quantitative evidence that influenza and RSV coexists throughout the ARI high season through superinfection. Our results might represent a tool to analyze year-to-year changes in the relative fitness between RSV and influenza due to influenza vaccination.

Spatial and Temporal Malaria Risk Profiles

The modern era of Amazon frontier expansion in Brazil witnessed the introduction of large-scale colonization projects focused on agriculture and wide-ranging human settlement, as well as the construction of infrastructure, such as roads and dams. These initiatives led to massive human migration, substantial environmental transformation, and severe malaria transmission. Interactions between development efforts, agricultural colonization, environment and health, at given levels of socioeconomic conditions, are very complex and demand a multidisciplinary analysis to serve as the basis for rational and successful policies. The talk will focus on a specific settlement project, and present a spatially explicit methodological approach that combined spatial analysis, geostatistical tools, and fuzzy sets, in a multidisciplinary way, in order to identify the most important factors impacting transmission. Results revealed that during the early stages of frontier settlement transmission was mainly driven by environmental risks, consequential to ecosystem transformations that promote larval habitats of Anopheles darlingi. With the advance of forest clearance and the establishment of agriculture, ranching, and urban development, malaria transmission was substantially reduced, and risks of new infection were largely driven by human behavioral factors.

Some effects of host movement in vector-borne disease systems

Host movements can have a profound impact on the transmission of vector-borne diseases because they can increase or reduce he rate of contact between hosts and vectors. It is clear that host movement can introduce pathogens to new environments, but models suggest that it can also increase or decrease the basic reproduction number (R0) within an environment by influencing the contact rates between hosts and infected vectors or between vectors and infected hosts. There are two distinct types of movement that are relevant in this context. They can be characterized as commuting and migration. The distinction is that migration envisions hosts changing the location of their primary residence, while commuting envisions that each host maintains a particular location of residence but visits other locations in the course of routine activities. These two types of movement require different models and may have different effects. This talk will review some models and results for the effects of host movement in vector-borne disease systems.


Within Host Dynamics of HIV and Malaria Co-infection

Malaria and HIV are among the most serious global health problems of our time. Together, malaria and HIV/AIDS cause more than 4 million deaths worldwide each year. Co-infection occurs in sub-Saharan Africa because there are wide geographical and epidemiological overlaps. Adverse effects of either infection on the other could have serious implications. In this talk, we propose a mathematical model to study the dynamics of immune responses to both malaria and HIV within a host of co-infection. The goal is to investigate the effect of HIV infection on malaria by studying the blood-stage dynamics of co-infection in individual hosts and incorporating red blood cells, CD4+ T cells, malaria parasitemia, HIV and immune effectors into a mathematical model. Numerical simulations demonstrate that HIV increases the risk of severe clinical malaria infection with higher density of parasitemia and more likely acute fever. (This talk is based on a joint manuscript with Dongmei Xiao).

Identifiability and interacting scales in modeling disease dynamics

Disease processes often involve interacting factors at multiple scales, which can affect both how we build models of these systems and the data sets needed to estimate model parameters. In this talk I will discuss some examples of disease transmission models that depend on processes at scales ranging from cellular to environmental, including cholera and human papillomavirus (HPV).

Crimean-Congo Hemorrhagic Fever: Why Do We Need a Model?

Crimean-Congo hemorrhagic fever (CCHF) is a fatal viral infection described from Africa, Asia, Southeastern Europe, and the Middle East1. The CCHF virus (CCHFV) belongs to the genus Nairovirus in the family Bunyaviridae, and causes severe disease in humans, with a reported case fatality rate of 3-30%. Humans can become infected through the bites of ticks, by contact with patients' body fluids, or by contact with blood or tissues from viremic livestock. Some occupational groups, including health care workers (HCW) are under risk of CCHF infection. Health care related CCHF infections were reported in Pakistan, United Arabic Emirates, South Africa, Iran, India, Tajikistan and Turkey. The greatest risk factor, however, is working with animals. The tick attaches itself to cattle, sheep, and goats. Around 30 countries in Africa, Asia, and Europe have reported CCHF. The tick ventures no further than 50° north latitude, which cuts across Russia, the Ukraine, and central Europe and France; the latter two regions are not considered to be at any immediate risk, the vector is present but there is no serological evidence of CCHF.



As with all vector-borne diseases, several ecological and anthropocentric factors are likely to affect the disease’s occurrence: increases in bush-type habitats, for example, and increases in wild animal populations or decreases in domestic animal populations. The first documented outbreak is a case in point. CCHF was initially recognized in 1944. USSR forces had driven the Germans out of the Crimea. During the occupation, farming activities had fallen into abeyance. People stopped hunting hares, and pastures became overgrown. When the Soviets recovered the Crimea, its soldiers, new settlers to the region, began to fall sick. (In 1969, the same virus was found to be responsible for a 1956 outbreak in the Congo, hence the name).



Changing patterns of agriculture and flood controls may also have played a part. In the Soviet Union, agriculture was collectivised and flood plains converted to farmland. Affected parts of central Anatolia had been more or less abandoned in the late 1990s due to terrorist activity. Hunting and farming resumed in 2001, and ticks were able to fasten upon the influx of cattle and sheep. The following year, Turkey confirmed its first case of CCHF and numbers have steadily increased ever since.



There are at least four reasons why we might want to use mathematical models to study CCHF.



1.Modeling can help us to gain a qualitative understanding of the dynamics of the disease and, in this way, help us to improve our intuition.



2.Second, by highlighting key uncertainties and gaps in our knowledge models may suggest observational or experimental studies that would improve our understanding of key aspects of the whole system. This is likely to be particular important in the area of understanding the vector dynamics where major uncertainties exist for CCHF. Since models can also be considered to be hypotheses about the systems, by confronting models with data we can effectively choose between competing hypotheses.



3.Third, models can help in the selection and evaluation of control policies. This can be done by employing models as statistical tools used to estimate the effect of interventions that have been made (and, equally importantly, to quantify the uncertainty in these estimates). Having quantified the effect of individual interventions, we can then go on to use models to ask “what-if� questions, using models predictively to determine the expected effect of hypothetical combinations of interventions. More generally, by enabling us to identify the most critical parameters affecting the behavior of the system, models can help us in setting priorities and identifying the most cost-effective control policies. Indeed, the use of dynamic models is essential for accurate economic analyses of control measures for infectious diseases.



4.Fourth, there is the potential to use models for forecasting the future of epidemics. Though popularly imagined as one of the main uses of models (perhaps by analogy to the models used to derive weather forecasts) this is one of the least developed areas in the infectious disease modeling literature, although there is increasing interest in this application.



One of the most useful concepts in infectious disease epidemiology is the case reproduction number: the average number of secondary cases caused by a primary case. For a tick-borne disease, we can define R0 as the average number of secondary infections in hosts from one primary infected host (when all hosts and ticks are susceptible) or, equivalently, as the average number of infectious ticks that arise from a single infected tick in a susceptible population. A simple SEIR modeling framework could be illustrated.



In many cases it is useful to estimate R0. The estimate will tell us how close we are to a risking a major epidemic (if R0 is currently below one) and allow precautionary measure to be taken. If R0 is greater than one the estimate tells us how much an intervention would have to do to bring about control or eliminate the chance of a major epidemic. An approach that has proved useful for other diseases is to estimate R0 from the distribution of the number of cases from clusters of transmission.



When more detailed surveillance data are available other approaches can be used to provide much better estimates of R0 and to assess the impact of interventions.



A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease

A new model is developed for linking the within- and between-host dynamics. The model is motivated by studying the disease dynamics of Toxoplasma gondii, in which the parasite’s life cycle includes interactions with the environment. We postulate the infection process to depend on the size of the infective inoculum that susceptible hosts may acquire by interacting with a contaminated environment. Because the dynamical processes of the within- and between-host systems occur on different time scales, the model behaviors can be analyzed by using a singular perturbation argument. We define new reproductive numbers for the within-host and between host dynamics for both the isolated systems and the coupled system. Particularly, the reproduction number for the between-host (slow) system dependent on the parameters associated with the within-host (fast) system in a very natural way. We show that these reproduction numbers determine the stability of the infection-free and the endemic equilibrium points. The model is capable of generating a backward bifurcation.

Modeling The Blood Stage Infection In Malaria: Advantages Of Discrete Versus Continuous Approaches

The blood stage of a malaria infection is the final step of the dual-host multi-stage disease. It is at this stage that most symptoms manifest and where the outcome is critical for the future disease trajectory toward either chronic infection or death. The blood stage is marked by the interplay between malarial merozoites, the erythropoietic system, and the immune system. Failure to properly up-regulate erythropoiesis results in anemia, while an improper immune response may lead to chronic infection that is characterized by recrudescence or relapse.


The production of red blood cells (RBCs) by the erythropoietic system takes about 5 days in our model organism, Macaca mulatta, and the RBCs normally remain in the blood stream for about 100 days. During this life cycle, only RBCs of the early age-classes are prone to merozoite invasion. Upon invasion, growth of the tropozoites into schizonts and the subsequent release of about 14 to 20 new merozoites take about 48 hours for the infecting parasite, Plasmodium cynomolgi. A computational systems analysis of the processes involved in the dynamics of RBCs in malaria demonstrated that the blood stage events are strongly dependent on different time delays and the structure of age-classes among the RBCs.


In this workshop presentation, we will discuss the advantages and disadvantages of using: ordinary differential equation (ODE) models with and without age-classes; delay differential equations (DDE); or discrete recursive models with age-classes. DDEs and ODEs with age-classes are well suited for the generation of delays, but lack the required flexibility to properly address issues associated with the constantly changing differentiation time of RBC precursors. By contrast, discrete recursive models allow the proper movement of all cells through their life cycle, while also allowing variables to be associated with dynamically changing delays, amplification ratios, and different types of injuries or infections, including malaria.


Epidemiology of tick-borne Rickettsia spp.

The incidence of tick-borne rickettsial disease in the southeastern United States has been rising steadily through the past decade, and the range expansions of tick species and tick-borne infectious agents, new and old, has resulted in an unprecedented mix of vectors and pathogens. The results of an ongoing 5-year surveillance project describe the relative abundance of questing tick populations in southeastern Virginia. Since 2009, more than 100,000 questing ticks of a variety of species have been collected from vegetation in a variety of habitats, with Amblyomma americanum constituting over 95% of ticks collected. We found that 26.9–54.9% of A. americanum ticks tested were positive for Rickettsia amblyommii, a non-pathogenic symbiont of this tick species. Rickettsia parkeri was found in 41.8–55.7% of Amblyomma maculatum ticks. The rate of R. parkeri in A. maculatum ticks is among the highest in the literature and has increased in the 2 years since R. parkeri and A. maculatum were first reported in southeastern Virginia. Additionally, R. parkeri is started to be found in A. americanum ticks throughout the region. While this is at extremely low prevalence, the sheer abundance of these ticks may increase the encounters with rickettsial agents with the potential for increased risk to human health.

The Malaria Host-Pathogen Interaction Center: a Systems Biology Coalition

The Malaria Host-Pathogen Interaction Center is led by investigators from Emory University, the University of Georgia (UGA), the Georgia Institute of Technology (GA Tech), and the Centers for Disease Control and Prevention (CDC), and includes collaborators from around the world. The project involves the longitudinal analysis of malaria infections in several non-human primate (NHP) models using high throughput technologies including immune profiling, functional genomics, proteomics, lipidomics, and metabolomics to generate data on host-pathogen interactions and an improved understanding of pathogenesis. In addition, the MaHPIC aims to develop metabolomic profiles from cross-sectional samples of human malaria infections from geographically diverse malaria endemic countries with a variety of epidemiological settings, and also consider broader systems based studies through such collaborations. The team is developing mathematical models of the parasite and host dynamics, as well as their interactions, to develop approaches to the prediction of various malarial clinical outcomes. Datasets will be deposited into a repository system that will feed a relational database (e.g., MaHPIC-DB) making the data accessible for bioinformatics, modeling and ongoing analysis and deeper investigation by the broad research community.

Systems biology of epidemiology From genes to environment

Traditional epidemiological models consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). These models are challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: Simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus causing individual to belong to multiple compartments simultaneously. (ii) Antigenic diversity and variation: Antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, and antigenic diversity, defined as antigenic differences between pathogens in a population, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission. This talk explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics in environmental transmission. A basic propagation number is calculated that could guide public health policy.

Flu in ducks and water - a multiscale modeling study

It has recently been suggested that for avian influenza viruses, prolonged persistence in the environment plays an important role in the transmission between birds. In such situations, influenza virus strains may face a trade-off: They need to persist well in the environment at low temperatures, but they also need to do well inside an infected bird at higher temperatures. Here, we report an analysis of fitness for avian influenza A viruses across scales, focusing on the phenotype of viral persistence. Taking advantage of a unique dataset that not only reports environmental virus persistence, but also strain-specific viral kinetics from duck challenge experiments, we show that the environmental persistence phenotype of a strain does not impact within-host infection dynamics and virus load. We thereby establish that for this phenotype, the scales of within-host infection dynamics and between-host environmental persistence do not interact: the virus can optimize fitness on each scale without cross-scale trade-offs. Instead, we confirm the existence of a temperature-dependent persistence trade-off on a single scale, with some strains optimizing environmental persistence in water at low temperatures while others reduce sensitivity to increasing temperatures.

Parallels between metapopulations and disease dynamics

Within host dynamics in diseases is essentially the same as dynamics within metapopulations in an ecological context. I will review results from metapopulation models, and draw parallels to disease dynamics. I will emphasize both similarities and differences. The goal will be to see how various assumptions about within host (equivalently within patch) dynamics reduce the complexity of the model and study and lead to models which can be studied analytically.

Reflections on predation, resources, and the linking of within-host pathogen dynamics to epidemiological processes

Pathogens in a population of hosts in effect live, and dispersing among, habitat ‘patches’ (viz., individual hosts), with the twist that the patches have their own dynamics, which in turn can be perturbed by the pathogens. Population dynamics in patchy environments quite generally is governed by the interplay of local within-patch conditions (such as resource supply) and coupling via dispersal among patches. Dispersal is a two-edged sword – emigration from occupied patches is required to colonize empty patches, but drains individuals from occupied patches, potentially lowering population size there. In this talk I will reflect on comparable processes that may arise in host-pathogen systems. First, I will argue that a consideration of host density-dependence and resource availability can alter expectations about how predation modulates infectious disease prevalence. A laboratory study of viral dynamics in host cell culture will provide an empirical illustration. Second, I will explore epidemiological models which include analogues of emigration (permitting transmission among hosts) impacting within-host pathogen dynamics.

Insights into Plasmodium vivax from spatial maps of human gene polymorphisms: Duffy blood group and G6PD deficiency.

Over a third of the world’s population lives at risk of potentially life-threatening Plasmodium vivax malaria infections. Unique aspects of this parasite’s biology and interactions with its human host make it harder to control and eliminate than the better studied Plasmodium falciparum parasite. The spatial epidemiology of two human genetic systems associated with these traits has been investigated in a multi-scale, model-based framework to generate estimates of populations of risk of P. vivax infection, and assessments of associated therapeutic risks.


First, the two key SNPs determining expression of the Duffy blood group were modelled to map the prevalence of Duffy phenotypes globally. The Duffy antigen is the only known erythrocyte receptor for P. vivax infection, and was used as a proxy indicator of population susceptibility to infection. The maps are discussed in light of reports of apparent Duffy-independent transmission.


Second, the global epidemiology of G6PD enzyme deficiency – both its phenotypic prevalence and genetic heterogeneity – is mapped. A geostatistical framework structured around the gene’s X-linked inheritance generated global estimates of G6PD deficiency prevalence, and estimates of affected population numbers. Poorly quantified risks from this spatially heterogeneous enzyme deficiency currently hinder widespread use of primaquine, a drug necessary for progress towards malaria elimination, particularly against the relapsing P. vivax life-stages.


These examples illustrate the positive contribution that integrating spatial epidemiological human genetic data can make in supporting the evidence-base for strategic planning for control of an infectious disease, thereby attempting to bridge the gap between basic biological research and the health sciences.


Within-host to population-level modeling of mycoplasmal conjunctivitis in wild birds

The pathogenic bacterium Mycoplasma gallisepticum jumped from poultry into North American House Finch populations during the early 1990s, and has since proven to be an accessible system in which to study the many faces of emerging infectious diseases in vertebrates. In this talk I'll begin by introducing the system, then I'll discuss some sources of individual-level variation in this system (and likely many others) including some results obtained by "scaling up" from the individual level. Then, I'll discuss the use of models to address questions at the population level including evolutionary dynamics and the importance of a novel virulence trade-off present in this system which is likely a factor driving evolutionary dynamics of other parasites with mobile host species.

Functional genomics of Malaria host-pathogen interaction center

The functional genomics core of the Malaria Host-Pathogen Interaction Center (MaHPIC) is using RNA-Seq to jointly profile gene expression in host non-human primate and Plasmodium parasite transcriptomes from peripheral blood samples during an infection cycle. I will report results from the first experiment, a modeling of relapsing malaria involving the macaque and P. cynomolgi, where we have seven time points from four individual macaques. As well as documenting among-individual variability and responses that cycle during phases of relapse, I will report on analytical methods leading toward integration of diverse types of omic data, principally transcriptomic, metabolomic, lipidomic, and immunological.

Ecological dynamics of a salmon parasite

In this talk I will outline the impact that parasitic sea lice have on the ecology of pacific salmon and the role that parasite spill over and spill back with aquaculture has taken in modifying the ecology of pacific salmon. These modifications are far reaching, and include changes in salmon returns, establishment of nonlinear population thresholds such as Allee effects, and shifts in predator prey dynamics. My talk will involve a mixture of modelling and data, based on over a decade of intensive field work.

Transmission of Cholera in the Far North Region of Cameroon - A Model-Guided Exploration

Cholera was first reported in West Africa in early 1970s and became endemic in the region since then. In 2010, one of major cholera epidemics occurred in West Africa and in the Lake Chad area (covering Cameroon, Nigeria, Chad, and Niger) more than 57,000 reported cases and 2,466 deaths were reported. In the Far North Region of Cameroon, the worst-hit region in the Lake Chad area, more than 9,400 cases and 600 deaths were reported. Yet, little is known on how the disease was transmitted and spread in the region. In this study, we first explore temporal patterns of cholera outbreaks and their associations with environmental factors (e.g. rainfall and temperature) based on 15-year’s (1996 – 2011) cholera cases reported weekly in the Far North Region. A wavelet approach is used to account for noisy and non-stationary nature of the cholera outbreak data and possibly transient relationships between cholera transmission and environmental factors. We then explore possible transmission mechanisms underlying the 2010 major cholera outbreak in the Far North using a mathematical model. Through extending the classic susceptible-infected-recovered (SIR) framework, we develop a meta-community model to assess how socio-environmental factors, in particular rainfall and human movement, might contribute to the cholera transmission in the Far North Region. The analyses have offered some important insights into drivers associated with the cholera transmission in the region and, guided by the modeling explorations, we have proposed some priorities for field epidemiological and environmental studies on ground.


The molecular epidemiology of P. vivax in Papua New Guinea

In co-endemic areas, the risk of infections and disease with P. vivax decreases more rapidly with age than that of P falciparum, indicating a substantially more rapid acquisition of immunity to infections with P. vivax. By genotyping all PCR-positive infections in a cohort of children it is possible to directly measure the incidence of genetically distinct bloodstone infections (i.e. molecular force of (bloodstone) infections, molFOB). By applying these methods to cohort of children 1-3 years of age, we found that they experience 2.5-times as many genetically distinct P. vivax (molFOB=14.0) than P. falciparum infections (molFOB=5.5) and that children with the highest exposure show fastest decrease decrease incidence of clinical P. vivax episodes. In P. falciparum, where immune acquisition if still limited, children with high exposure have the highest risk of illness. By clearly long-lasting dormant liver stage parasites (i.e. hypnzoites) in 247 of 504 children aged 5-10 year, we were subsequently able to show that relapses from hypnozoites infections account for ~80% of blood stage infections. A comparable proportion of relapses vs. primary infections we found by stochastical modelling of in-host dynamics of P. vivax infections the cohort of children 1-3. This indicated that P. vivax relapses contribute significantly to the higher P. vivax molFOI and more rapid acquisition of immunity.

Optimal Control and Analysis of a Coupled ODE/PDE Immuno-epidemiological Model.

Optimal control can be used to design intervention strategies for the management of infectious diseases, and has been applied in immunological and epidemiological models separately. We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE. Existence and uniqueness of solution to the between-host model is established, and an explicit expression for the basic reproduction number of the between-host model is derived. Stability of disease-free and endemic equilibria of the between-host model is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed. Numerical simulations based on the forward-backward sweep method are obtained.

Deterministic within-host viral dynamics

In this talk, I will review the basic features of deterministic models of within-host viral dynamics. I will discuss the global asymptotic behavior of such models, and extensions of the stability results to models including multi-strain competition, antiviral treatment, and immune response.


Interference particles as resistance-proff antiviral therapy: Cost-benefit tradeoff and the evolutionary conflict between two biological scales

A major obstacle to the development of anti-viral therapies is the rapid evolution of viral resistance. HIV models provide a good context for investigation of means for resistance-proofing treatments. A proposed resistance-proof system for HIV therapy involves the use of defective copies of the virus, therapeutic interfering particles (TIPs), which interfere with viral action at a cellular scale by co-opting viral resources in order to further their own spread, but which do not spread in the absence of the virus. This mechanism of action allows for viral suppression not only within a single cell, but also throughout an HIV-infected host, and across a population of hosts. Extending a previously described multiscale model for TIP action, we show that TIPs can invade existing populations of HIV-infected individuals if the initial prevalence of HIV is large enough, and investigate the emergence of resistance within a population after a successful course of TIP intervention. We then show that by adjusting the relative rates of TIP and HIV transcription, we can produce suppression of HIV within a population while simultaneously hampering the spread of TIP resistant mutants and promoting the spread of susceptible ones. In this parameter region, the benefit of resistance and its cost are tightly related, with the cost exceeding the benefit. This stands in contrast to the case of antiviral drugs, where the two are independent and vary over a broad range. We propose experiments in chemostat and nonhuman primate models to test the key aspects of our findings.

Within Host Dynamics of HIV and Malaria Co-infection

Malaria and HIV are among the most serious global health problems of our time. Together, malaria and HIV/AIDS cause more than 4 million deaths worldwide each year. Co-infection occurs in sub-Saharan Africa because there are wide geographical and epidemiological overlaps. Adverse effects of either infection on the other could have serious implications. In this talk, we propose a mathematical model to study the dynamics of immune responses to both malaria and HIV within a host of co-infection. The goal is to investigate the effect of HIV infection on malaria by studying the blood-stage dynamics of co-infection in individual hosts and incorporating red blood cells, CD4+ T cells, malaria parasitemia, HIV and immune effectors into a mathematical model. Numerical simulations demonstrate that HIV increases the risk of severe clinical malaria infection with higher density of parasitemia and more likely acute fever. (This talk is based on a joint manuscript with Dongmei Xiao).

Potential amplification of an HIV epidemic due to drug resistance

The use of antiretroviral therapy (ART) is the most efficient measure in controlling the HIV epidemic. However, emergence of drug-resistant strains can reduce the potential benefits of ART. The viral dynamics of drug-sensitive and drug-resistant strains at the individual level may play a crucial role in the emergence and spread of drug resistance in a population.

We investigate the effect of the viral dynamics within an infected individual on the epidemiological dynamics of HIV using a nested model that links both dynamical levels. A time-dependent between-host transmission rate that receives feedback from a model of two-strain virus dynamics within a host is incorporated into an epidemiological model of HIV. We analyze the resulting dynamics of the model and identify model parameters such as time when ART is initiated, fraction of cases treated, and the probability that a patient develops drug resistance, as having the greatest impact on total infection and prevalence of drug resistance. Importantly, for small values of the risk of a patient developing drug resistance, increasing the fraction of cases treated can increase the cumulative number of infected individuals. Such a pattern is the result of the balance between not treating a patient and having future cases still sensitive to treatment, and treating the patient and increasing the chances for future (untreatable) drug-resistant infections.

The current modeling framework incorporates important aspects of virus dynamics within a host into an epidemic model. This approach provides useful insights on the drug resistance dynamics of an epidemic of HIV, which may assist in identifying an optimal use of ART.

Target reproduction number and its application

A new quantity called the target reproduction number is defined to measure the magnitude of matrix entries reduction or enlargement in order to control the spectral radius of a nonnegative matrix. New expressions for target reproduction numbers are derived and illustrated using mathematical models for within-host virus infection and waterborne diseases in a heterogeneous environment.

Author: Zhisheng Shuai (University of Central Florida) and Pauline van den Driessche (University of Victoria)

Systems-scale and integrative "omic" analysis of host-pathogen interactions in malaria

As part of the Malaria Host-Pathogen Interaction Center, our goal is to study and model the response of both host and pathogen to the course of malarial infection, treatment, and recurrence or recrudescence, using multiple levels of "omic" data. Detailed mathematical models are a desired ultimate product of our study of malaria, and while there are certainly some intuitive candidate systems for such modeling, it is not necessarily clear a priori which other systems should be modeled, nor which variables are important to include in those models. Our goal is to exploit the multiple levels of systems-scale datasets being generated in our center to identify such candidates for detailed models and follow-up experiments.


The main task in achieving this goal is discovery of novel, unknown interactions between our measured variables. This can be accomplished via a number of classes of approaches, including statistical analyses and machine learning. Here, we will focus on our machine learning approaches to identifying subnetworks of interesting interactions, specifically using probabilistic graphical models to construct interaction networks. Within this domain, two of the biggest obstacles to accomplishing our goal are 1) computational tractability given the high dimensional variable space, and 2) integrating multiple disparate data types, each with potentially different scales of variable space dimensionality (tens of measurements vs. tens of thousands of measurements) and different time scales, such that no data type dominates or is dwarfed in importance. We will present our algorithmic work addressing these problems, along with applications to the malaria data that has been generated by our center to date.


Disease invasion of community networks with environmental pathogen movement

Consider a set of communities (patches), connected to one another by a network. When can disease invade this network? Intuitively, this should depend upon both the properties of the communities, as well as on the network structure. Here we make this dependence explicit for a broad class of disease models with environmental pathogen movement. In particular, the rooted spanning trees of the network and a generalization of the group inverse of the graph Laplacian play fundamental roles in determining the ability of disease to invade. This is joint work with Z. Shuai, M. Eisenberg, and P. van den Driessche.

Tracking dynamic innate immune responses in experimental malaria infection

Experimental malaria infections in non-human primates (NHPs) are a prime setting to assess the changing biological conditions associated with disease, notably with regards to the host immune system. While much attention has been focused on T-cell and B-cell dependent ("adaptive") responses that are key to vaccine development and long-term protection in malaria, relatively little is known of the involvement of the innate immune system. Here, we will highlight a novel approach that addresses this gap in knowledge, and will show early data obtained as part of the Malaria Host Pathogen Interaction Center (MaHPIC) consortium at Emory University, Georgia Tech and University of Georgia (PI: Mary Galinski, Co-PIs: Alberto Moreno, Jessica Kissinger). By tracking functional responses mounted by the innate immune system in malaria-infected NHPs, we show that this arm of the immune system is mobilized to a major extent during the course of infection. This data is the first of its kind and will be discussed in relation to integration with other omics technologies and use in building mathematical models that include both adaptive and innate host immunity.


Chet Joyner, Mary Galinski, Rabindra Tirouvanziam, Emory University

Coexistence or Replacement of two Subtypes of Influenza

From observations, a pandemic subtype of influenza A sometimes replaces but sometimes coexists with the previous seasonal subtype. For example, the 1957 pandemic subtype H2N2 replaced the seasonal subtype H1N1; whereas after 1977 subtypes H1N1 (from the pandemic) and H3N2 continue to coexist. In an attempt to understand these alternatives, a model for the dynamics of influenza during an epidemic season is formulated taking into account cross immunity depending on the most recent seasonal infection. This cross immunity is assumed to reduce susceptibility to related strains of the seasonal subtype, and to wane with time due to virus drift. The population reaches an equilibrium distribution in susceptibility after several seasons, and then a pandemic subtype appears to which individuals in the population all have the same cross immunity. Threshold conditions for coexistence or replacement are derived from the model, with the conditions depending on the reproduction number of seasonal influenza and the level of cross immunity between the seasonal and pandemic subtypes. This is a preliminary report on joint work with S.M. Asaduzzaman and J. Ma.

Scientific Overview and Challenges

With this presentation I will try to set the stage for the modeling efforts to be discussed in the workshop. As the title “From Within Host Dynamics to the Epidemiology of Infectious Disease� directly suggests, infectious diseases involve many scales, with respect to time, space, and organization, with the latter spanning the range from molecules to global effects. While a hallmark goal of systems biology is the integration of heterogeneous information across multiple scales and levels, our computational modeling capabilities are clearly not quite ready to cover all aspects of infectious diseases. Thus, the workshop is hoped to address three fundamental questions, namely:


1. How can modeling help us bridge the gaps between scales or levels of organization?


2. How can we make optimal use of very diverse data (from traditional biology and biochemistry, high-throughput –omics methods, physiology, clinical observations, host-parasite interactions, disease spread, interventions) in order to deepen our understanding of disease dynamics and adaptation, by both hosts and parasites, and to devise treatment options that are generic or even personalized, and executable at a global scale?


3. What can modelers of different sub-disciplines within the span between within-host-dynamics and epidemiology learn from each other?


In addition to these research questions, the workshop is hoped to discuss means of “bidirectional� education between the often separate groups of clinicians and experimentalists on one side and computational analysts on the other. This education should give clinicians and experimentalists a feel for what is achievable with modern modeling tools and help modelers frame specific and relevant biological questions for analyses that offer genuine added value.


As this meeting of expert minds is a workshop rather than a conference, polished answers are not necessarily the goal. Instead, the workshop will be a success if the participants collectively take account of where we are, what we can do with today’s methods, where we want to be in N years, and what we need to do to get there.



TBD

Abstract coming soon.

Mathematical model on Malaria with multiple strains of pathogens

Vector-borne diseases are usually associated with infections caused by multiple strains (genotypes) of pathogens. For example, there are several strains of malaria protozoa spreading in different regions. Globalization and modern transportation raise a natural concern of possible epidemics caused by multiple strains of parasites in one region. In this study, we use mathematical models to explore such a possibility. Firstly, we propose a model to govern the within-host dynamics of two strains. Analysis of this model practically excludes the possibility of co-persistence (or super-infection) of the two strains in one host. Then we move on to set up another model to describe the dynamics of disease transmission between human and mosquito populations without the co-infection class (using the results for the within-host model). By analyzing this model, we find that co-endemic caused by both strains in a single region are possible within certain range of model parameters. This is a joint work with Xingfu Zou.

Posters

A within-host model for dengue infection and disease severity

Here we present within-host mathematical models of dengue infection that are the first to our knowledge to quantitatively describe how the interaction of the immune system with dengue virus leads to increased cytokine production and an increased probability of manifesting severe disease. We first formulate a minimal model that can reproduce known viral features of primary symptomatic infections. We then use this model, and a variant thereof, to determine whether the dominating theories

explaining why a secondary heterologous infection results in severe disease can reproduce features of a secondary symptomatic infection that differ in their relation to a primary infection. Finally, we show that the minimal model is able to reproduce described clinical markers of disease severity, and use the model to understand the effectiveness and limitations of these markers.

Using network modeling to investigate rabies spread through a raccoon population

The number and duration of contacts made between individuals in wildlife populations can be highly heterogeneous and this can vary by season. Contact networks are a powerful tool for understanding the transmission of diseases through populations where contact structure is variable. We used raccoon social interaction data, collected using proximity logging collars in suburban Illinois, to construct adjacency matrices specifying the connections made between raccoons over one year. These matrices formed the basis of our network model, which we used to simulate the spread of rabies through the raccoon population. We found that raccoon contact patterns were dependent on season and sex and could be grouped into long-term and short-term interactions.

Co-authors: Jennifer Reynolds, Ben Hirsch, Stanley Gehrt, Suzanne Prange, Stephanie Hauver

Host-to-host variation of ecological niches in polymicrobial Otitis Media infection

Communities of multiple microbial species routinely co-exist with humans and other animals. The structure and dynamics of these host-associated microbiota depend on multitude of factors including host immune response and available nutrients in the microenvironment. Otitis Media (OM) presents a unique system to study basic mechanisms of host-microbiota interactions where the infection of the middle ear is caused by a small number of bacterial species. Using a combination of population dynamic models, a Maximum Entropy (MaxEnt) based inference scheme, and experimental data in OM infection in chinchillas and in vitro culture experiments we quantify the ecological niches and host-to-host variations of these niches for infection of the middle ear by the two major OM infection causing bacterial species, nontypeable Haemophilus influenzae (NTHI) and Streptococcus pneumoniae(Sp). We find that the nature of the interspecies interaction between the bacterial species critically regulates the host-to-host variations of the ecological niches and seemingly unrelated niches, such as interspecies interactions and the host immune response can become correlated in a host population. The latter finding suggest a potential mechanism that the host immune response employ to lead to selection of specific strains of bacterial species in a host population.

Transmission and immune dynamics of endemic foot-and-mouth disease in Cameroon by serotype

Foot-and-mouth disease (FMD) is an apthoviral infection of cloven-hoofed animals for which evidence of infection or vaccination can lead to strict trade embargos. While pathology and epidemic dynamics have been studied, less research has been conducted in natural, endemic settings. Here, we present age-structured seroprevalence data from cattle in the Far North Region of Cameroon, where at least three serotypes of FMDV are endemic. We use catalytic models to estimate the force of infection and duration of the antibody response for each serotype. These findings identify serotype-specific FMDV dynamics under endemicity and provide information to inform veterinary intervention.

The loss of history and the strength of density-dependence in microbial community dynamics

Elucidating the mechanisms that govern microbial community composition, dynamics and function are rooted in modeling population dynamics. Regulatory processes directly translate into changes in the growth rate of a population. Dynamical models for the growth rate of a population, when fitted to temporal fluctuations of a given species’ abundances in communities, have proven to yield reliable insights to the ecological processes that give rise to temporal feedback and regulation of population densities. Identifying the changes in demography and intra-specific competition that a sudden environmental change can trigger has been an elusive goal of population dynamics modeling. Here, we develop of a population dynamics model that includes a process-based formulation of a change point either in the demography, strength of density dependence, influence of the environment, or all of these factors simultaneously. In the model, this change occurs after the population has been fluctuating for some generations in a given environment. The full mathematical treatment of this model results in precise mathematical formulae that specify exactly how previous demographic and intra-specific competition coefficients influence the dynamics after the change point. Of special significance is that these formulae show how the historical properties of a population’s growth and the variability in population abundances are completely determined by the strength of the density-dependent processes after the change point. Moreover, these analyses show that a time series of population abundances right after the breakpoint contain substantial information to determine not only the properties before the change, but also whether the population is going to stabilize around a new population size and if so, how long it is going to take to arrive to such stationary behavior. Remarkably, the speed of the loss of historical properties of the dynamic behavior of a population’s growth is given directly by a simple function of the strength of density-dependence after the change point. The model reveals that the stability properties of the population before a change (the location of the equilibrium population size and the variability around it) loom large after the change only if the new density-dependent coefficient is relatively weak.

Parallels between metapopulations and disease dynamics
Systems biology of epidemiology From genes to environment
Spatial and Temporal Malaria Risk Profiles
Some effects of host movement in vector-borne disease systems
Ecological dynamics of a salmon parasite
Flu in ducks and water - a multiscale modeling study
Insights into Plasmodium vivax from spatial maps of human gene polymorphisms: Duffy blood group and G6PD deficiency.
Tracking dynamic innate immune responses in experimental malaria infection
Within-host to population-level modeling of mycoplasmal conjunctivitis in wild birds
Mathematical model on Malaria with multiple strains of pathogens
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Parallels between metapopulations and disease dynamics
Alan Hastings

Within host dynamics in diseases is essentially the same as dynamics within metapopulations in an ecological context. I will review results from metapopulation models, and draw parallels to disease dynamics. I will emphasize both similarities and

video image

Systems biology of epidemiology From genes to environment
Juan Gutierrez

Traditional epidemiological models consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). These models are challenged when the within-host dynamic

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Some effects of host movement in vector-borne disease systems
Chris Cosner

Host movements can have a profound impact on the transmission of vector-borne diseases because they can increase or reduce he rate of contact between hosts and vectors. It is clear that host movement can introduce pathogens to new environments, b

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Ecological dynamics of a salmon parasite
Mark Lewis

In this talk I will outline the impact that parasitic sea lice have on the ecology of pacific salmon and the role that parasite spill over and spill back with aquaculture has taken in modifying the ecology of pacific salmon. These modificati

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Flu in ducks and water - a multiscale modeling study
Andreas Handel

It has recently been suggested that for avian influenza viruses, prolonged persistence in the environment plays an important role in the transmission between birds. In such situations, influenza virus strains may face a trade-off: They need

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Tracking dynamic innate immune responses in experimental malaria infection
Rabindra Tirouvanziam

Experimental malaria infections in non-human primates (NHPs) are a prime setting to assess the changing biological conditions associated with disease, notably with regards to the host immune system. While much attention has been focused on T

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Spatial and Temporal Malaria Risk Profiles
Marcia Castro

The modern era of Amazon frontier expansion in Brazil witnessed the introduction of large-scale colonization projects focused on agriculture and wide-ranging human settlement, as well as the construction of infrastructure, such as roads and

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Insights into Plasmodium vivax from spatial maps of human gene polymorphisms: Duffy blood group and G6PD deficiency.
Rosalind Howes

Over a third of the world€™s population lives at risk of potentially life-threatening Plasmodium vivax malaria infections. Unique aspects of this parasite€™s biology and interactions w

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Modeling The Blood Stage Infection In Malaria: Advantages Of Discrete Versus Continuous Approaches
Luis Fonseca

The blood stage of a malaria infection is the final step of the dual-host multi-stage disease. It is at this stage that most symptoms manifest and where the outcome is critical for the future disease trajectory toward either chronic infectio

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Systems-scale and integrative "omic" analysis of host-pathogen interactions in malaria
Mark Styczynski

As part of the Malaria Host-Pathogen Interaction Center, our goal is to study and model the response of both host and pathogen to the course of malarial infection, treatment, and recurrence or recrudescence, using multiple levels of "om

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Epidemiology of tick-borne Rickettsia spp.
Holly Gaff

The incidence of tick-borne rickettsial disease in the southeastern United States has been rising steadily through the past decade, and the range expansions of tick species and tick-borne infectious agents, new and old, has resulted in an un

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Within-host to population-level modeling of mycoplasmal conjunctivitis in wild birds
Paul Hurtado

The pathogenic bacterium Mycoplasma gallisepticum jumped from poultry into North American House Finch populations during the early 1990s, and has since proven to be an accessible system in which to study the many faces o

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Identifiability and interacting scales in modeling disease dynamics
Marisa Eisenberg

Disease processes often involve interacting factors at multiple scales, which can affect both how we build models of these systems and the data sets needed to estimate model parameters. In this talk I will discuss some examples of disease tr

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Disease invasion of community networks with environmental pathogen movement
Joe Tien

Consider a set of communities (patches), connected to one another by a network. When can disease invade this network? Intuitively, this should depend upon both the properties of the communities, as well as on the network structure. Here we m

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Thresholds for Extinction in Stochastic Models of Infectious Diseases: Importance of Time and Location
Linda Allen

Relations between Markov chain models and differential equation models for infectious diseases near the infection-free state are derived. Approximation of the Markov chain model by a multitype branching process leads to an estimate of the pr

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Optimal Control and Analysis of a Coupled ODE/PDE Immuno-epidemiological Model.
Eric Numfor

Optimal control can be used to design intervention strategies for the management of infectious diseases, and has been applied in immunological and epidemiological models separately. We formulate an immuno-epidemiological model of coupled <

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Deterministic within-host viral dynamics
Sergei Pilyugin

In this talk, I will review the basic features of deterministic models of within-host viral dynamics. I will discuss the global asymptotic behavior of such models, and extensions of the stability results to models including multi-strain comp

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Scientific Overview and Challenges
Eberhard Voit

With this presentation I will try to set the stage for the modeling efforts to be discussed in the workshop. As the title €œFrom Within Host Dynamics to the Epidemiology of Infectious Disease€? directly suggests