Contents -- Preface -- Zhien Ma: Some Recent Results on Epidemic Dynamics Obtained by Our Group -- Abstract -- 1 Basic knowledge on epidemic dynamics -- 1.1 Adequate contact rate and incidence -- 1.2 Basic reproduction number -- 2 Epidemic models with vaccination -- 3 Epidemic models with quarantine strategy -- 4 Epidemic models with complicated structures -- 5 Epidemic models with natural age and infection age structures -- 6 Epidemic models with time dependent coefficients -- 7 Epidemic models combining with population ecology -- 8 Epidemic models combining with ecotoxicology -- 9 The phenomenon of stability switches on some epidemic models with time delay -- 10 Study on HIV / AIDS -- 11 Modeling and study for SARS transmission and control in China -- References -- Fred Brauer, Jianhong Wu: Modeling SARS, West Nile Virus, Pandemic Influenza and Other Emerging Infectious Diseases: A Canadian Team's Adventure. -- Abstract -- 1 Introd uction -- 2 Progresses on specific diseases: scientific contributions -- 2.1 SARS -- 2.2 Pandemic influenza -- 2.3 West Nile Virus -- 3 Other progress and networking activities -- 4 Summer school/intensive course & CDM -- 4.1 Summer school/intensive course, seminar series -- 4.2 International collaboration -- 4.3 The future -- 5 Final remarks -- Acknowledgement -- References -- Julien A rino: Diseases in Metapopulations -- Abstract -- 1 Foreword - Notations -- 2 Metapopulations -- 2.1 Introduction -- 2.2 The connection graph -- 2.3 Dynamics in the vertices -- 2.3.1 Properties of the movement matrix -- 2.3.2 Case of an irreducible movement matrix -- 2.3.3 Case of a reducible movement matrix -- 3 Methodological aspects -- 3.1 The models under consideration -- 3.1.1 Simple SEIRS -- 3.1.2 SEIRS for multiple species -- 3.1.3 SEIRS model with residency patch -- 3.1.4 Types of movement matrices -- 3.2 Well-posedness.

3.2.1 Existence and uniqueness of solutions -- 3.2.2 Nonnegativity and/or positivity of solutions -- 3.2.3 Boundedness of solutions -- 3.3 Behavior of the demographic component -- 3.4 Existence of a disease free equilibrium (DFE) -- 3.5 Reproduction number and local stability of DFE -- 3.5.1 Simple SEIRS -- 3.5.2 SEIRS with multiple species -- 3.5.3 SEIRS with residency patch -- 3.6 Global stability of the disease free equilibrium -- 3.6.1 Simple SEIRS -- 3.6.2 SEIRS with multiple species -- 3.6.3 SEIRS with residence patch -- 3.7 Existence of mixed equilibria -- 3.7.1 Model with classic movement -- 3.7.2 Model with residency patch -- 3.8 Bounds on Ro -- 3.8.1 SEIRS with residency patch -- 3.9 Further problems -- 3.9.1 Existence of endemic equilibria -- 3.9.2 Understand the effect of movement -- 4 Diseases in metapopulations - A review -- 4.1 Focus of the review -- 4.2 Early works -- 4.3 Kermack-McKendrick-type models -- 4.4 Migration models -- 4.5 Model including residency patch -- 4.6 New directions -- 4.6.1 True patch heterogeneity -- 4.6.2 Models with infinite dimensional aspects -- 5 Cond usion -- References -- Fred Brauer: Modeling the Start of a Disease Outbreak -- 1 Introduction -- 2 The network corresponding to a disease outbreak -- 3 Transmissibility -- 4 Some examples of contact networks -- 5 Conclusions -- References -- Troy Day: Mathematical Techniques in the Evolutionary Epidemiology of Infectious Diseases. -- Abstract -- 1 Introduction -- 2 Mathematical models of pathogen evolution -- 2.1 The underlying epidemiological model -- 2.2 Invasion analysis technique -- 2.3 Price equation technique -- 3 Discussion -- Appendix -- References -- Zhilan Feng, Dashun Xu, Haiyun Zhao: The Uses of Epidemiological Models in the Study of Disease Control. -- Abstract -- 1 Introduction -- 2 Models with quarantine and isolation.

3 Reproductive numbers of the general model -- 4 Comparison of models with different sojourn distributions -- 5 Conclusion -- References -- John W. Glasser, Maureen Birmingham: Assessing the Burden of Congenital Rubella Syndrome and Ensuring Optimal Mitigation via Mathematical Modeling. -- Abstract -- 1 The diseases -- 2 Risk of infection -- 3 Assessing the burden -- 3.1 Assessment methods -- 3.2 Assessment examples -- 4 Mitigation strategies -- 5 Evaluating the options -- 5.1 Dynamic modeling -- 5.2 Modeling example -- 6 Monitoring the impact -- 7 Summary -- Acknowledgments -- References -- Thanate Dhirasakdanon, Horst R. Thieme: Persistence of Vertically Transmitted Parasite Strains which Protect against More Virulent Horizontally Transmitted Strains -- Abstract -- 1 Introduction -- 2 A model with horizontal and vertical transmission -- 3 The persistence equilibrium -- 3.1 Uniqueness and existence -- 3.2 Global stability of the persistence equilibrium -- 4 The multiple strain model -- 5 The two strain model with one strain only vertically transmitted -- 5.1 Coexistence equilibrium -- 5.2 Dynamic coexistence -- 6 Global stability for constant contact function and per capita birth rate -- 7 Uniform strong coexistence -- Appendix: Elements of persistence theory -- Acknowledgement -- References -- Ying-Hen Hsieh: Richards Model: A Simple Procedure for Real-time Prediction of Outbreak Severity. -- Abstract -- 1 Introduction -- 2 Logistic and Richards models -- 3 Single wave out break -- 4 Outbreaks with multiple waves -- 5 Conclusions and remarks -- References -- James Watmough: The Basic Reproduction Number and the Final Size of an Epidemic -- 1 Introduction -- 2 A general disease transmission model -- 3 The basic reproduction number -- 4 The final size of a simple epidemic -- 5 A final size inequality for a general model -- 6 Examples.

6.1 The constant rate SIR epidemic model -- 6.2 Simple compartmental models -- 6.3 The SLIAR model for influenza -- 6.4 A discrete delay -- 7 Further Reading -- References -- K.P. Hadeler: Epidemic Models with Reservoirs -- Abstract -- 1 Introduction -- 2 SIR model in a given population -- 3 Singular perturbation -- 4 SIR model with demographic renewal -- 5 Homogeneous demographic model -- 6 Special homogeneous system -- 7 Case fatality -- Acknowledgement -- References -- Hongbin Guo, Michael Y. Li, Zhisheng Shuai: Global Stability in Multigroup Epidemic Models -- Abstract -- 1 Introduction -- 2 Preliminaries -- 3 Proof of Theorem 1.1 -- Acknowledgments -- References -- Wendi Wang: Epidemic Models with Time Delays -- Abstract -- 1 Introduction -- 2 Mathematical modeling -- 2.1 Models without demographic structure -- 2.2 Model with vital dynamics -- 3 Analysis of local stability -- 3.1 Models with constant coefficients -- 3.2 Models with delay-dependent coefficients -- 4 Liapunov direct methods -- 5 Conditions of disease persistence -- 6 Summary -- References -- Shenghai Zhang: A Simulation Approach to Analysis of Antiviral Stockpile Sizes for Influenza Pandemic. -- Abstract -- 1 Introduction -- 2 Methods -- 3 Model -- 4 Results -- 5 Conclusion and discussion -- References -- Peter Buck, Rongsong Liu, Jiangping Shuai, Jianhong Wu, Huaiping Zhu: Modeling and Simulation Studies of West Nile Virus in Southern Ontario Canada -- Abstract -- 1 Introduction -- 2 The model formulation -- 3 Surveillance data and numerical simulations -- 3.1 Birds -- 3.2 Mosquitoes -- 3.3 Bird ecology in the absence of WNV -- 3.4 Bird ecology with WNV -- 3.5 Simulation results, with the best fit non crow family birds recover rate r = 1/365 -- 3.6 Remarks on the preference parameter -- 4 Discussions -- Acknowledgement -- References.