### Organizers

Spread of infectious diseases remains a major threat. It has been a central and current challenge in mathematical biology to show how mathematical modeling and analysis can facilitate understanding of mechanisms of disease transmissions and thereby, provide guidance for designing disease control strategies under rapid social and environmental changes. Among the various factors that affect the disease spread are spatial dispersal and time lags, with the former due to the increasing inter-connections of the world/environmental changes and the latter as a result of the disease latency (e.g., in Influenza, HIV and and Malaria), postponed relapses of diseases (e.g., Herpes and TB), the stage-development of hosts, as well as the delay in implementing intervention strategies. The worldwide spread of SARS in 2003-04 and the 2009 H1N1 influenza pandemic clearly demonstrate the importance of incorporating time delay and spatial dispersal into human infectious disease models, and the rapid spread and establishment of West Nile virus and Lyme disease in North American is another example showing how spatial movement of migratory animals facilitates the spatial propagation. In order to reflect the aspects of spatial dispersal and time lag, ordinary and partial differential equation models need to be replaced by models with infection age and spatial structure, leading to systems of delay differential equation with spatial diffusion/dispersal which are infinite dimensional by nature. Disease evolution and ecology also have significant impact on the spread dynamics and need to be incorporated into models.

This workshop aims to bring together applied mathematicians, biologists and researchers from health institutes/departments to (i) examine and refine exiting models; (ii) present new results on disease models with time lags, spatial dispersal and evolutionary factors incorporated; (iii) exchange ideas among researchers in the related areas; (iii) discuss future directions in research of disease dynamics; and (iv) initiate collaborations in focused areas related to global air traffic network; seasonally migratory birds; impact of environmental changes on animal dispersal networks and disease spread.

### Accepted Speakers

Monday, October 10, 2011 | |
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Time | Session |

09:00 AM 09:45 AM | Ben Bolker - An overview of spatial dispersal models (no description available) |

09:45 AM 10:30 AM | Howie Ginsberg - Differences in the ecology of tick-borne v. mosquito-borne pathogens, and the implications for modeling, surveillance, and management (no description available) |

11:00 AM 12:00 PM | Odo Diekmann - Discussion on related modeling issues Group discussion |

02:15 PM 03:00 PM | Nicholas Ogden - Modelling vector-borne disease spread - the example of Lyme disease in Canada The USA has suffered an epidemic of Lyme disease, which began in the late 1970s and continues to this day. In Canada, Lyme disease is an emerging infection due to recent expansion of the range of the tick vector Ixodes scapularis, which may in part be due to a warming climate. Here we describe how a comprehensive understanding of the ecology of I. scapularis, its hosts and the pathogens it transmits, have allowed us to predict the scope and direction of potential range expansion of Lyme disease with projected climate change. This knowledge has also allowed us to raise model-based hypotheses for how climate change may affect evolutionary processes of I. scapularis-borne microparasites and drive pathogen emergence. Together, these studies will allow us to limit the public health impact of Lyme disease and other zoonoses by prediction and early warning of tick-borne pathogen risk. However, we discuss here in general the strengths and limitations of modelling vector-borne disease spread for public health purposes. |

03:30 PM 05:00 PM | Jean Tsao - Discussion Group discussion |

03:30 PM 05:00 PM | Suzanne Lenhart - Day One Discussion Day One Discussion |

Tuesday, October 11, 2011 | |
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Time | Session |

09:00 AM 09:30 AM | Suzanne Lenhart - Optimal control of spatial and temporal epidemic models Optimal control of two types of epidemic models with spatial and temporal features will be presented. Both examples will model rabies in raccoons. One model will be discrete in space and time and the other is a system of partial differntial equations. |

10:30 AM 12:00 PM | Rongsong Liu - Discussion on disease control issues Group discussion |

01:30 PM 02:00 PM | Odo Diekmann - Run for your Life In 1927 Kermack and McKendrick introduced and analyzed a rather general epidemic model (nota bene : their model takes the form of a nonlinear renewal equation and the familiar SIR model is but a very special case !). The aim of this lecture is to revive the spatial variant of this model, as studied in the late seventies by Horst Thieme and myself (see the AMS book 'Spatial Deterministic Epidemics' by L. Rass and J. Radcliffe, 2003). The key result is a characterization of c_0 , the lowest possible speed of travelling waves and the proof that c_0 is also the asymptotic speed of epidemic propagation. |

02:00 PM 02:30 PM | Xiaoqiang Zhao - A Reaction-Diffusion Malaria Model with Incubation Period in the Vector Population Malaria is one of the most important parasitic infections in humans, and more than two billion people are at risk every year. To understand how the spatial heterogeneity and extrinsic incubation period of the parasite within the mosquito affect the dynamics of malaria epidemiology, we propose a nonlocal and time-delayed reaction-diffusion model. We then introduce the basic reproduction ratio for this model and show that it serves as a threshold parameter that predicts whether malaria will spread. A sufficient condition is obtained to guarantee that the disease will stabilize at a positive steady state eventually in the case where all the parameters are spatially independent. Further, we use two vaccination programs to simulate the efficiency of spatial control strategies. If time permits, I will also mention our more recent work on the global dynamics of an extended system, which incorporates a vector-bias term into this model. This talk is based on joint works with Drs. Yijun Lou and Zhiting Xu. |

03:00 PM 05:00 PM | Xingfu Zou - Discussion Group discussion |

Wednesday, October 12, 2011 | |
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Time | Session |

09:00 AM 09:30 AM | Maria Diuk-Wasser - Modeling human risk for tick-borne pathogens in the United States (no description available) |

09:30 AM 10:00 AM | Tim Reluga - Assessing spatially-dependent risks of disease-emergence Infectious disease ecology is perennially concerned with risks from new and emerging infectious diseases. SARS in humans, white nose syndrome in bats, and (possibly) colony collapse disorder in honey bees are just 3 examples from the last decade. But patterns of disease emergence do not appear to be spatially uniform. Rather, they seem to occur in locations where particular confluences of conditions favor establishment. In this talk, I will describe our investigations extending stuttering-chain emergence theories based on branching processes to include spatial heterogeneity and dispersal processes. The theory can be applied to a wide variety of dispersal models, and used to anticipate emergence hot-spots. |

10:45 AM 11:15 AM | Jen Owen - Host-level drivers of infectiousness and susceptibility in birds: implications for emergence and spread of pathogens In the last century, there has been an unprecedented increase in the numbers of emerging infectious diseases for humans. Approximately 60% of these diseases are naturally maintained by animals (i.e. zoonotic), primarily wildlife. Mathematical models are typically employed to predict how a disease will spread through a population. Yet, many of these models assume a homogenous population, in which all individuals are equally susceptible and have same probability of transmitting infection. Organisms exhibit heterogeneity in their ability to maintain pathogens; some individuals exhibit high pathogen loads (i.e. 'supershedders') whereas others maintain low pathogen loads. An individual's ability to maintain and amplify a pathogen may be determined by a suite of intrinsic and extrinsic factors, including age, sex, behavior, immunity, genetics, and environmental stressors. I will discuss our current research studying how variation in a bird's energetic condition, stress hormone profile, and migratory status affects their response to viral pathogens. Incorporating this heterogeneity into epidemic models will likely produce an outcome that is a better representation of reality. |

11:15 AM 11:45 AM | Lydia Bourouiba - The dynamics of "contact" via coughing and sneezing Following the introduction of a pathogen in a population of susceptible hosts, the nature of the "contact" between infected and non-infected members of the population becomes critical in shaping the outcome of the epidemics; nevertheless, the mechanisms leading to contact and transmission of common infectious diseases remain poorly understood. Here, we discuss how a combination of theoretical and experimental biofluid dynamic approaches can help shed light on the dynamics of contact for respiratory diseases. |

Thursday, October 13, 2011 | |
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Time | Session |

09:00 AM 09:30 AM | - Cholera dynamics past and present Cholera was one of the most feared diseases of the 19th century, and remains a serious public health concern today. I will discuss some results on parameter identifiability and estimation for cholera models, present data from cholera epidemics in 19th century London, Angola 2006, and the current outbreak in Haiti, and discuss ongoing efforts to model these outbreaks. |

09:30 AM 10:00 AM | Pauline van den Driessche - Dynamics of some cholera models There have been several recent outbreaks of cholera, which is a bacterial disease caused by the bacterium Vibrio cholerae. It can be transmitted to humans directly by person-to-person contact or indirectly via contaminated water. To better understand the dynamics of cholera, a general compartmental model is discussed that incorporates these two transmission pathways as well as multiple infection stages and pathogen states. A basic reproduction number is identified that gives a sharp threshold for the global dynamics and an estimate of the control required for eradication. Further models that incorporate temporary immunity and hyperinfectivity using distributed delays are formulated. Numerical simulations show that oscillatory solutions may occur for parameter values taken from the literature on cholera data. |

10:30 AM 12:00 PM | Stephen Cantrell - Discussion Group discussion |

01:30 PM 02:00 PM | Wendi Wang - Basic reproduction numbers for reaction-diffusion epidemic models The basic reproduction number and its computation formulae are established for epidemic models with reaction-diffusion structures. It is proved that the basic reproduction number provides the threshold value for disease invasion in the sense that the disease-free steady state is asymptotically stable if the basic reproduction number is less than unity and the disease is uniformly persistent if it is greater than unity. On the basis of these theoretical results, three epidemic models for rabies, lyme disease and West Nile transmissions are analyzed to reveal the better strategies for these diseases. With the aid of numerical simulations, we find that the reduction of heterogenous infection is beneficial because the more heterogenous infection leads to the higher value of basic reproduction numbers. Moreover, influences from spatial configurations of disease infection and diffusion coefficients are investigated. This is a joint work with Xiaoqiang Zhao. |

02:00 PM 02:30 PM | James Watmough - Marine invasions (no description available) |

02:30 PM 03:00 PM | Wenzhang Huang - Dynamics of an SIS Reaction-Diffusion Epidemic Model for Disease Transmission (no description available) |

03:30 PM 05:00 PM | Chris Cosner - Discussion Group discussion |

Friday, October 14, 2011 | |
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Time | Session |

09:00 AM 09:30 AM | Stephen Gourley - Insecticide resistance and its implications for mosquito and malaria control Mosquitoes can rapidly develop resistance to insecticides, which is a big problem in malaria control. Current insecticides kill rapidly on contact, but this leads to intense selection for resistance because young adults are killed. Of considerable current interest is the possibility of slowing down or even halting the evolution of resistance. Biologists believe that much weaker selection for resistance can be achieved if insecticides target only old mosquitoes that have already laid most of their eggs. This strategy aims to exploit the fact that most mosquitoes do not live long enough to transmit malaria, due to a long latency stage for the malaria parasite in the mosquito. I will present the results of some mathematical work using stage structured population models that can make predictions about the delayed onset of resistance in the mosquito population when they are subjected to an insecticide that only acts late in life. I will also summarise some ongoing work that includes the malaria disease dynamics and also the consequences of mosquito control using larvicides. Larvae can become resistant to larvicides, but the evolutionary cost of this acquired resistance may be reduced longevity as adults, which reduces the likelihood of the parasites completing their developmental stages and thus can actually benefit malaria control. This is a joint collaboration with Rongsong Liu, Chuncheng Wang and Jianhong Wu. |

09:30 AM 10:00 AM | Shigui Ruan - Spatio-Temporal Dynamics in Disease Ecology and Epidemiology We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian that mimics human commuting behavior and (ii) Eulerian that mimics human migration. We determine the basic reproduction number R0 for both modeling approaches and study the transmission dynamics in terms of R0. We also study the dependence of R0 on some parameters such as the travel rate of the infectives. |

Name | Affiliation | |
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Aavani, Pooya | pooya.aavani@ttu.edu | Mathematics and Statistics, Texas Tech University |

Aggarwal, Nitish | aggarwal.nitish@gmail.com | Mathematics, The Ohio State University |

Allan, Brian | ballan@illinois.edu | Entomology, University of Illinois at Urbana-Champaign |

Arino, Julien | arinoj@cc.umanitoba.ca | Mathematics, University of Manitoba |

Bolker, Ben | bolker@math.mcmaster.ca | Math & statistics and Biology, McMaster University |

Bourouiba, Lydia | lydia.bourouiba@math.mit.edu | Mathematics, Massachusetts Institute of Technology |

Brown, Leone | lbrown@life.bio.sunysb.edu | Ecology and Evolution, SUNY |

Cantrell, Steve | rsc@math.miami.edu | Mathematics, University of Miami |

Castorena, Chris | crc34@duke.edu | Computional Biology, Duke University |

Cosner, Chris | c.cosner@math.miami.edu | Department of Mathematics, University of Miami |

Dai, Liman | ldai6@uwo.ca | Applied Math, University of Western Ontario |

Darbha, Subrahmanyam | Darbha.1@osu.edu | Epidemiology, The Ohio State University |

Diekmann, Odo | O.Diekmann@uu.nl | Mathematics, Utrecht University |

Diuk-Wasser, Maria | maria.diuk@yale.edu | Division of Epidemiology of Microbial Diseases, |

Feng, Zhilan | zfeng@math.purdue.edu | Mathematics, Purdue University |

Gao, Daozhou | dzgao@math.miami.edu | Francis I. Proctor Foundation, University of California, San Francisco, Francis I. Proctor Foundation, UCSF |

Ginsberg, Howard | hginsberg@usgs.gov | USGS Field Station, |

Gourley, Stephen | s.gourley@surrey.ac.uk | Mathematics, University of Surrey |

Hickling, Graham | ghicklin@utk.edu | The Center for Wildlife Health, University of Tennessee |

Huang, Wenzhang | huangw@email.uah.edu | Mathematical Sciences, University of Alabama |

Jennings, Rachel | rfarris4@uwyo.edu | Mathematics, University of Wyoming |

Joo, Jaewook | jjoo1@utk.edu | Physics, University of Tennessee |

Kelly, Michael | mkelly14@utk.edu | Mathematics, University of Tennessee |

Lai, Xiulan | xlai3@uwo.ca | Department of Applied Mathematics, University of Western Ontario |

Lenhart, Suzanne | lenhart@math.utk.edu | |

Li, Jing | li_j@math.psu.edu | Mathematics, Pennsylvania State University |

Liang, Song | liang.113@osu.edu | College of Public Health, The Ohio State University |

Liu, Rongsong | Rongsong.Liu@uwyo.edu | Mathematics, University of Wyoming |

Lou, Yijun | ylou@yorku.ca | Department of Mathematics and Statistics, York University |

Mandal, Sandip | smandal@ccmb.res.in | Mathematical Modelling and Computational Biology, Centre for Cellular and Molecular Biology |

Medlock, Jan | medlock@clemson.edu | Biomedical Sciences, Oregon State University |

Moritz, Mark | moritz.42@osu.edu | Anthropology, The Ohio State University |

Nakakawa, Juliet | njuliet12@gmail.com | Mathematics, Stellenbosch University |

Ngonghala, Calistus | ngonghala@yahoo.com | National Institute for Mathematical and Biological Synthesis, University of Tennessee |

Njagarah, John Boscoh | johnhatson@sun.ac.za | Department of Mathematical Sciences, Stellenbosch University |

Ogden, Nicholas | nicholas_ogden@phac-aspc.gc.ca | Zoonoses Division, Public Health Agency of Canada |

Owen, Jen | owenj@msu.edu | Fisheries and Wildife and Large Animal Clinical Sciences, Michigan State University |

Reluga, Tim | treluga@math.psu.edu | Department of Mathematics, Pennsylvania State University |

Requena-Anicama, David | d.requena.a@gmail.com | Bioinformatics Unit, Universidad Peruana Cayetano Heredia |

Rong, Libin | rong2@oakland.edu | Mathematics and Statistics, Oakland University |

Rost, Gergely | rost@math.u-szeged. hu | Bolyai Institute, University of Szeged |

Ruan, Shigui | ruan@math.miami.edu | Department of Mathematics, University of Miami |

Shi, Junping | shij@math.wm.edu | Mathematics, College of William and Mary |

Shuai, Zhisheng | zshuai@uvic.ca | Mathematics and Statistics, University of Victoria |

Singh, Anuraj | anurajiitr@gmail.com | Department of Mathematics, Indian Institute of Technology |

Sui, Daniel | sui.10@osu.edu | Department of Geography, The Ohio State University |

Te Beest, Dennis | dennis.te.beest@rivm.nl | centre for infectious disease control, |

Tsao, Jean | tsao@msu.edu | Fisheries and Wildlife, Michigan State University |

Vaidya, Naveen | nvaidya2@uwo.ca | Applied Mathematics, University of Western Ontario |

van den Driessche, Pauline | pvdd@math.uvic.ca | Mathematics and Statistics, University of Victoria |

Wang, Wendi | wendi@swu.edu.cn | Mathematics and Statistics, Southwest University |

Watmough, James | watmough@unb.ca | Department of Mathematics and Statistics, University of New Brunswick |

Xiao, Yanyu | yxiao26@uwo.ca | Applied Mathematics, University of Western Ontario |

Zhao, Xiaoqiang | xzhao@math.mun.ca | Math, |

Zou, Xingfu | xzou@uwo.ca | Applied Mathematics, University of Western Ontario |

The key result is a characterization of c_0 , the lowest possible speed of travelling waves and the proof that c_0 is also the asymptotic speed of epidemic propagation.

This is a joint collaboration with Rongsong Liu, Chuncheng Wang and Jianhong Wu.

**Basic reproduction numbers for reaction-diffusion epidemic models**

Wendi Wang The basic reproduction number and its computation formulae are established for epidemic models with reaction-diffusion structures. It is proved that the basic reproduction number provides the threshold value for disease invasion in the sense that the

**Spatio-Temporal Dynamics in Disease Ecology and Epidemiology**

Shigui Ruan We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain

**Insecticide resistance and its implications for mosquito and malaria control**

Stephen Gourley Mosquitoes can rapidly develop resistance to insecticides, which is a big problem in malaria control. Current insecticides kill rapidly on contact, but this leads to intense selection for resistance because young adults are killed. Of considerable cu

**Dynamics of an SIS Reaction-Diffusion Epidemic Model for Disease Transmission**

Wenzhang Huang (no description available)

**Run for your Life**

Odo Diekmann In 1927 Kermack and McKendrick introduced and analyzed a rather general epidemic model (nota bene : their model takes the form of a nonlinear renewal equation and the familiar SIR model is but a very special case !). The aim of this lecture is to rev