Multiscale Dynamics of Infections

Multiscale challenges in modelling the initial spatial spread of an infectious pathogen
Julien Arino (Mathematics, University of Manitoba)

In a world where global travel and movement of goods is the norm, understanding the initial phase of spread of an infectious pathogen is paramount. Indeed, determining which locations are the potential "next targets" of a budding epidemic helps public health authorities allocate resources more effectively, which can in turn bring the nascent event under control before it reaches epidemic scale. However, the initial spatial spread is governed by processes occurring at a variety of scales which act in the origin location, during transport and in the destination location. In this talk, I will discuss some of the issues arising in this context and present some (very partial) methodology that has been developed to address these issues.

Hybrid models predict emergent dynamics of multiscale cell populations
Neda Bagheri (Chemical & Biological Engineering, Northwestern University)

Computational models are essential tools that can be used to simultaneously explain and guide biological intuition. With increasingly high-resolution, high-throughput, and dynamic experimental data, computational biologists are better equipped to develop informed models that to characterize complex cellular responses and direct experimental design. I introduce an agent-based model as an intuitive, modular, and flexible framework to study emergence of heterogeneous cell populations. We use this framework to interrogate the inherent multiscale nature of cells—reinforcing how “the whole is greater than the sum of its parts”—and to predict cell population dynamics from the composition of simpler biological modules. Elucidating the compositionality problem is fundamental to advancing our understanding of basic science; to promoting the impact of synthetic biology; and to designing precise dynamic therapeutic strategies.

Transition Dynamics Convey Key Programs in Cellular Populations
Caleb Bastian (Princeton University)

The epithelial-mesenchymal transition (EMT) is a key cellular program of growth and development and of mature cells, such as wound healing. Evidence for its role in pathology, such as cancer invasion, has been accumulating following from intensive study, yet little is known about the dynamics of the transition per se. Using a multidisciplinary approach, this talk explores the dynamics of the transition and its role in conveying distinct gene programs. The global spatiotemporal distribution of metastatic (dysregulatory) burden is found to be critically sensitive to key non-linear dynamics.

Exploring the role of geographic scale on foot and mouth disease outbreaks
Lindsay Beck-Johnson (Department of Biology, Colorado State University)

Foot and mouth disease (FMD) is a viral infection of cloven-hoofed animals, including livestock species such as cattle, pigs, and sheep. FMD is highly transmissible and outbreaks in non-endemic countries are very expensive. Therefore, there is interest from policy makers in understanding potential outbreaks and identifying ways to reduce losses. The United States Disease Outbreak Simulation (USDOS) is a simulation model that allows for exploration of national-scale infection patterns and control of potential U.S. FMD outbreaks in cattle. USDOS is a premises-level model, incorporating information on both local spread and long-distance transmission events, which are informed by cattle shipment networks. In this presentation, I will discuss how the national scale outcomes of potential FMD outbreaks in the U.S. are influenced by local, regional, and national factors and how these may be altered by control actions.

Different FMD outbreak models incorporate geographic scale in different ways and in systems, like FMD, where there are multiple quality models, it can be difficult for policy makers to select a single model on which to base high-stakes decisions. Here I will present an international collaborative project on the development of a multi-model ensemble that includes four different FMD models that are commonly used in policy. Ensemble modeling methods provide a standardized and transparent way of producing a single, interpretable projection from multiple model outputs. Here we use the multi-model ensemble and data from the initial weeks of the 2001 U.K. FMD outbreak to explore whether the method could improve the accuracy of the model predictions early in an epidemic before the outcome of the outbreak is known.

Incorporating within-host heterogeneity into transmission models
Lauren Childs (Mathematics, Virginia Polytechnic Institute and State University)

Mathematical models are a key tool in the study of the spread of infectious diseases such as influenza, malaria and dengue. In particular, transmission models have been successful at determining the most promising intervention strategies, despite the fact that many of these models assume all individuals experience identical infections. Here, we discuss the importance of incorporating heterogeneity into transmission models and consider when particular types of heterogeneities can reasonably be ignored.

Modelling coupled within host and population dynamics of R5 and X4 HIV infection
Chirove Faraimunashe (Mathematics, Statistics and Computer Science, University of KwaZulu-Natal)

Most existing models have considered the immunological processes occurring within the host and the epidemiological processes occurring at population level as decoupled systems. We present a new model using continuous systems of non linear ordinary differential equations by directly linking the within host dynamics capturing the interactions between Langerhans cells, CD4[Formula: see text] T-cells, R5 HIV and X4 HIV and the without host dynamics of a basic compartmental HIV/AIDS model. The model captures the biological theories of the cells that take part in HIV transmission. The study incorporates in its analysis the differences in time scales of the fast within host dynamics and the slow without host dynamics. In the mathematical analysis, important thresholds, the reproduction numbers, were computed which are useful in predicting the progression of the infection both within the host and without the host. The study results showed that the model exhibits four within host equilibrium points inclusive of three endemic equilibria whose effects translate into different scenarios at the population level. All the endemic equilibria were shown to be globally stable using Lyapunov functions and this is an important result in linking the within host dynamics to the population dynamics, because the disease free equilibrium point ceases to exist. The effects of linking were observed on the endemic equilibrium points of both the within host and population dynamics. Linking the two dynamics was shown to increase in the viral load within the host and increase in the epidemic levels in the population dynami

A Categorization Framework for Multiscale Models of the Dynamics of Infections
Winston Garira

The development of multiscale models of the dynamics of infections is a scientific endevour whose progress has so far resulted in the development of a wide variety of multiscale models of the dynamics of infections with different structure and mathematical representations which are associated with the different levels of organization of an infectious disease system (cell level, tissue level, host level, etc.). In this talk I will present a framework for categorization of multiscale models of the dynamics of infections. Such a categorizarion framework is useful in categorizing and classifying the different types of multiscale models of infection dynamics and in turn in bring some order to the discussion on the structure of multiscale models of infectious disease systems. This categorization of the different types of multiscale models of infectious disease systems may be found useful as a basis for further refinement, in the discourse of multiscale modelling of the dynamics of infections. It will enable infectious disease modelers to discuss the general principles that should apply to each category of multiscale models. Instead of discussing these principles repeatedly whenever a multiscale model of an infectious disease system is being developed, infectious disease modelers will be able to refer to the generic discussion for the category of the multiscale model concerned, and focus instead on the application of that discussion to the particular multiscale model of an infectious disease system being developed, and on issues peculiar to that multiscale model. While this categorization cannot be claimed to be unique, I think that it constitutes a good starting point, which may be found useful as a basis for further refinement in the discourse of multiscale modelling of the dynamics of infections.

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System
Hayriye Gulbudak (Mathematics, University of Louisiana at Lafayette)

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influence the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission tradeoffs and evolution in vector-borne pathogen-host systems. Here we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley Fever and West Nile Virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the $mathcal R_0$ maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories, and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen $mathcal R_0$, but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.

Multiscale Systems Biology: A Case Study Linking Molecular Dynamics to Epidemiological Processes of Malaria
Juan B. Gutierrez (Mathematics, University of Georgia)

The advent of high-throughput molecular technologies in particular, and the broad availability of data, in general, have forced the quantitative biology community to rethink how to conceive, build, and validate mathematical models. In this talk I will demonstrate how molecular and cellular processes are related to the epidemiology of malaria. We will explore (i) asymptomaticity at the epidemiological level, (ii) telemetry analysis identifying a systemic response to the disease before traditional symptoms show, (iii) the cellular models that explain this phenomenon as an interaction between the immune system and infected red blood cells, (iv) mathematical models that link cellular and transcriptional time series, (v) transcriptomic analysis, and finally (vi) high-throughput in silico drug discovery to solve an epidemiological problem. All these linked analyses provide a comprehensive picture that no single scale can produce alone. The usefulness of models under this light takes on new meanings, and this broad scope requires the cooperation of scientists coming from very different intellectual traditions. In this talk we will also explore how an information system that delivers Adaptive Learning for Interdisciplinary Collaborative Environments (ALICE) is used to train scientists in this new normal.

Multiscale Modeling the Transmission of Infectitious Diseases
James Hyman (Mathematics, Tulane University)

Epidemiology of environmentally transmitted infections: models and empirical data
Renata Ivanek (Population Medicine and Diagnostic Sciences, Cornell University)

For environmentally-transmitted infections the contaminated environments, such as food, water, soil, objects, and contact surfaces, represent vehicles for transmission of the infection to susceptible hosts. The causative agents of these diseases exhibit rich dynamics in the host and in the environment and require modeling and empirical studies at both the host and pathogen scales. This presentation will describe what we have learned about the spread of these pathogens between the host populations and their environments, and about the pathogens’ dynamics in the heterogeneous environments. The focus will be on findings of compartmental and agent based models and selected empirical studies. Several human/animal pathogens, including Salmonella, pathogenic Escherichia coli and Listeria, will be used as examples. Finally, the existing knowledge gaps in terms of modeling and empirical data to support or validate models will be discussed.

A pandemonium of parasites: predictability in the face of complex parasite interaction networks?
Anna Jolles

Human activities are altering host-parasite interactions and their ecological context at unprecedented rates, reducing our ability to anticipate disease impacts and predict transmission dynamics in host populations of interest. These changes lend urgency to understanding the mechanisms underlying variation in disease dynamics, by developing data-driven models that scale up from within-host processes affecting parasite invasion and persistence, to population-level disease dynamics.

In this talk, I focus on interactions among co-infecting parasites as drivers of disease outcomes and dynamics. Using African buffalo and their parasite community as a model system, I demonstrate that co-infecting parasites contribute strongly to incidence and duration of concurrent infections, perhaps forming a modular interaction network. I propose trait-based community analysis as a possible approach for increasing the predictability of outcomes of parasite invasions, using Mycobacterium bovis, the causative agent of bovine TB, as a case study. M. bovis infection leads to changes in parasite infracommunity structure in buffalo, but few other parasites seem to affect the incidence of M. bovis itself. Instead, genetically driven variation in host defense responses against M. bovis underlies variation in infection risk. Linking ecological processes with evolutionary responses, I discuss how co-infection might be shifting both host and pathogen population genetic structure – an area in need of further investigation.

Pairwise survival analysis: Contact intervals, regression, and phylogenetics
Eben Kenah (College of Public Health, The Ohio State University )

When integrating epidemiologic data with pathogen phylogenetics, the likelihood for the transmission model is often a branching-process likelihood based on a generation interval distribution and offspring distribution. We show that a misspecified likelihood can lead to severely biased estimates with or without a pathogen phylogeny. Writing the likelihood as a survival likelihood with failure times in pairs---a process we call pairwise survival analysis---accounts for time spent at risk of infection. In a simple example with three infections, we show that a pairwise survival likelihood produces more accurate source attribution and parameter estimation. In a mass-action model with negligible depletion of susceptibles, the pairwise survival likelihood depends only on information about infected individuals in the limit of a large population. However, this asymptotic likelihood has cumulative hazard terms that have no counterpart in a branching process likelihood. As an example of the flexibility of pairwise survival analysis, we describe a pairwise accelerated failure time model that can be used to estimate covariate effects on infectiousness and susceptibility. This model---modified to account for the buildup of immunity---will be used to estimate the efficacy of the Ebola vaccine based on the WHO ring vaccination trial in Guinea. This trial collected data on individuals exposed to infection who escaped as well as Ebola virus genetic sequences. Finally, we describe a pruning algorithm for calculating an approximate likelihood using both epidemiologic data and a pathogen phylogeny. Pathogen genetics can improve statistical efficiency and reduce bias, but this depends on good epidemiologic study design and a good likelihood for transmission.

Modeling the temporal evolution of the host immune response to infection
Michael Kirby

We will present two explorations into to the temporal dynamics of the host immune response. The first concerns the real-time modeling telemetry data generated by collaborative cross (CC) mice. The CC mice are monitored in a healthy state for seven days and are subsequently challenged with a salmonella infection. Temperature and activity data is collected at one minute intervals and modeled in real time using a method for time-series prediction that also serves as a novelty detector to quantify time to symptoms and full blown infection. The analysis seeks to identify and characterize aspects of tolerance to high pathogen loads exhibited by certain CC lines. We are also exploring dynamical systems models to explain this phenomenon. The second study relates to the early prognosis of subject outcome in human challenges to influenza viruses. We demonstrate algorithms that can predict if a subject will become symptomatic, or not, as early as 5 hours after exposure. (The mice study is being conducted in collaboration with David Threadgill and Helene Andrews-Polymenis of Texas A&M. Aspects of the dynamical modeling are recent collaborations with Judy Day (UTK) and Helene Andrews-Polymenis.)

Transmission and infection dynamics of Clostridium difficile
Cristina Lanzas

Clostridium difficile is an anaerobic human pathogen that forms spores, produce toxins and resides in the gut. Clostridium difficile infection (CDI) is an important hospital acquired infection that causes diarrhea, pseudomembranous colitis, and possibly death. In the last decade, the incidence and severity of C. difficile infection has increased at alarming rates throughout North America, especially in the elderly. Antimicrobial therapy is often a strong and independent risk factor for CDI because it disrupts the indigenous microbiota, which provides protection against C. difficile colonization. Epidemiological and within host models for Clostridium difficile and integration of both scales will be discussed.

Analysis of the Plague at Eyam
Daniel Linder (Biostatistics, Georgia Health Sciences University)

The rodent-flea-human transmission route of Y. pestis is widely known and has been medically confirmed to cause the bubonic form of plague. However, the observed rapidity of plague outbreaks during the second pandemic appear to have happened on timescales that are not readily explained by this transmission mechanism alone. We propose a statistical method to analyze such data that is capable of distinguishing the important mechanisms of outbreak dynamics. We implement the methodology on data from the latter half of the outbreak at Eyam in the summer of 1666.

Challenges when building a continental scale livestock disease spread model: Animal movements, farm locations, and computation
Tom Lindstrom (IFM)

Applied epidemiological modeling offers powerful tools to inform policy decisions regarding control actions, identify spatial hotspots, or predict the course of an outbreak. However, modeling is often challenged by limited information about the system. For instance, in the USA, there are no federal databases with animal movements that can be used to model disease spread via these contacts. I will present some of our ongoing work to circumvent this issue by developing the United States Animal Movement Model (USAMM), which is parameterized based on interstate certificates of veterinary inspection and can be used to predict movement across the USA, including within state shipments.

In an international collaboration with researchers from Linköping University (Sweden), Colorado State University (USA), United States Department of Agriculture, and University of Warwick (UK), we connect USAMM predictions to a disease spread model (United States Disease Outbreak Simulator, USDOS), which also accounts for local spread, to simulate outbreak of livestock diseases. This faces another challenge: where are the farms? As with animal movements, there are no federal databases with farm locations, and the most detailed information available is census data from the National Agricultural Statistics Service (NASS) at the county level. Using predictions based on the Farm Location and Animal Population Simulator (FLAPS), I will present some of our work focused on determining whether fine-scale farm distribution matters when modeling disease outbreaks on the US farm population, using Foot and Mouth Diseases as an example. For this purpose, we use both analytical methods and stochastic simulations. The latter involves simulations among nearly 850000 farms, and efficient computation is crucial. I will also present an approach to speed up simulations for spatially explicit disease simulations.

Identifiability Issues of an Immuno-Epidemiological Model: The case of Rift Valley Fever Virus
Maia Martcheva (Mathematics, University of Florida)

We discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host–vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to fit multi-scale models to multi-scale data. For an immunological model, we use Rift Valley Fever Virus (RVFV) time-series data obtained from livestock under laboratory experiments, and for an epidemiological model we incorporate a human compartment to the nested model and use the number of human RVFV cases reported by the CDC during the 2006–2007 Kenya outbreak. We show that the immunological model is not structurally identifiable for the measurements of time-series viremia concentrations in the host. Thus, we study the scaled version of the immunological model and prove that it is structurally globally identifiable. After fixing estimated parameter values for the immunological model derived from the scaled model, we develop a numerical method to fit observable RVFV epidemiological data to the nested model for the remaining parameter values of the multi-scale system. For the given (CDC) data set, Monte Carlo simulations indicate that only three parameters of the epidemiological model are practically identifiable when the immune model parameters are fixed. Alternatively, we fit the multi-scale data to the multi-scale model simultaneously. Monte Carlo simulations for the simultaneous fitting suggest that the parameters of the immunological model and the parameters of the immuno-epidemiological model are practically identifiable.

Research performed in collaboration with Necibe Tuncer, Hayriye Gulbudak, and Vincent Cannataro.

Local and regional dynamics of arbovirus transmission: the role of mismatched spatial heterogeneity
Sean Moore (Bacterial Diseases Branch, Centers for Disease Control and Prevention)

Background: Mathematical models of transmission dynamics are routinely fitted to epidemiological time series, which must inevitably be aggregated at some spatial scale. Weekly case reports of chikungunya have been made available nationally for numerous countries in the western hemisphere since late 2013, and numerous models have made use of this data set for forecasting and inferential purposes. Motivated by an abundance of literature suggesting that the transmission of this mosquito-borne pathogen is localized at scales much finer than nationally, we fitted models at three different spatial scales to weekly case reports from Colombia to explore limitations of analyses of nationally aggregated time series data.

Methods: We adapted the recently developed DTK-Dengue model for modeling chikungunya virus (CHIKV) transmission, given the numerous similarities of these viruses vectored by a common mosquito vector. We fitted versions of this model specified at different spatial scales to weekly case reports aggregated at different spatial scales: (1) single-patch national model fitted to national data; (2) single-patch departmental models fitted to departmental data; and (3) multi-patch departmental models fitted to departmental data, where the multiple patches refer to municipalities within a department. We compared the consistency of simulations from fitted models with empirical data.

Results: We found that model consistency with epidemic dynamics improved with increasing spatial granularity of the model. Specifically, the sum of single-patch departmental model fits better captured national-level temporal patterns than did a single-patch national model. Likewise, multi-patch departmental model fits better captured departmental-level temporal patterns than did single-patch departmental model fits. Furthermore, inferences about municipal-level incidence based on multi-patch departmental models fitted to departmental-level data were positively correlated with municipal-level data that were withheld from model fitting.

Conclusions: Our model performed better when posed at finer spatial scales, due to better matching between human populations with locally relevant risk. Confronting spatially aggregated models with spatially aggregated data imposes a serious structural constraint on model behavior by averaging over epidemiologically meaningful spatial variation in drivers of transmission, impairing the ability of models to reproduce empirical patterns.

The population genentics of pathogen virulence
Todd Parsons

Life history theory provides a powerful framework to understand the evolution of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are very large and that one can neglect the effects of demographic stochasticity. In my talk, I will present an alternative approach, based in population genetics, which will explore the effects of finite population size on the evolution of pathogen virulence and transmission. I will show that demographic stochasticity introduces additional evolutionary forces that can affect qualitatively the dynamics and the evolutionary outcome. In particular, I will discuss scenarios where finite population size can either select for lower or higher virulence.

Modeling endemic foot-and-mouth disease in Cameroon
Laura Pomeroy (Veterinary Preventive Medicine, Ohio State University)

Foot-and-mouth disease virus (FMDV) threatens animal health and leads to considerable economic losses worldwide. Endemic disease dynamics occur throughout Asia and Africa; however, most models of infectious disease dynamics represent locations throughout North America, Europe, and Australia that experience epidemic dynamics or have been FMD-free for decades. This dichotomy has resulted in a void in our understanding of natural FMD dynamics. Therefore, we investigated disease dynamics in the Far North Region, Cameroon, where FMDV is endemic and five serotypes have been detected in cattle. First, we characterized and quantified serotype-specific transmission and immunodynamics in cattle. Second, we investigated if pastoral mobility plays a role in endemic maintenance. This work underscores the importance of using empirical data in models to understand processes that influence the transmission of infectious diseases at multiple scales.

Micro and macro SIR models
Grzegorz Rempala (Biostatistics, OSU)

Recently, there has been considerable interest in both inference and predictions for compartmental epidemic models on multiple physical scales, like, for instance, a single host and a population of hosts. Both viral invasions and global pandemics are often described by similar mathematical constructs known as SIR models. In this talk I will review some basic concepts related to such models across scales and present a simple unifying framework that allows to conceptually connect both deterministic (e.g., population level) and stochastic (e.g., molecular level) SIR models with the help of tools of statistical theory of survival analysis.

Dynamic Models of Malaria
Eberhard Voit (Dept. of Biomedical Engineering, Georgia Tech and Emory University)

Malaria is a complex disease that afflicts 200 million individuals worldwide and causes about 500,000 deaths per year. It is transmitted by Anopheles mosquitoes and caused by one of several Plasmodium species, which have a complicated life cycle that is distributed between the mosquito and the human host. The molecular events, host-pathogen interactions, physiological host responses, and the global reach of the disease create a truly multi-scale system. I will present five vignettes describing mathematical models of molecular and cellular events during malaria infections in non-human primates, which offer excellent models of the human disease processes. Three vignettes will focus on different aspects related to the dynamics of red blood cells and reticulocytes, whose disappearance is the dominant driver of malarial anemia, one of the most severe hallmarks of the disease. The other two vignettes will demonstrate how insights into the meaning of transcriptomic changes during the disease can be gained through models of concomitant processes at the metabolic and physiological levels.

This work is joint work with Luis L. Fonseca and Anuj Gupta.

A Hierarchy of Reduced Mathematical Models for Wolbachia Transmission in Mosquitoes to Control Mosquito-borne DiseasesZhuolin Qu (Mathematics, Tulane University)

We create and analyze a hierarchy of reduced models for the spread of a Wolbachia bacteria infection in mosquitoes that can help predict the effectiveness of efforts to control the spread of Zika, chikungunya, dengue fever and other mosquito-borne diseases. Mosquitoes that are infected with some strains of the Wolbachia bacteria are much less effective at transmitting zoonotic diseases. The infection will persist in a wild mosquito population only if the fraction of infected mosquitoes exceeds a minimum threshold. This threshold can be characterized as a backward bifurcation for a system of nine ordinary differential equations modeling the complex vertical transmission of the bacteria infection in a heterosexual mosquito population. Although the large system of differential equations capture the detailed transmission dynamics, they are difficult to analyze. We derive a seven-equation, a four-equation and a two-equation system of differential equations that are formulated in terms of the more accurate nine-equation model and capture the important properties of the original system. The reduced models preserve key dimensionless numbers, the ratios of infected and uninfected male and female mosquitoes, and accurately capture the backward bifurcation threshold.