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Deterministic and Stochastic Reaction-Diffusion Models in a Ring

For an epidemic to occur, infectious individuals have to generate at least one secondary infection before they die or recover. A simple model is introduced where epidemic states are possible when the number of secondary infections caused by an individual is less than 1. Models with varying levels of complexity in the population dynamics are introduced and the question of whether or not they force or drive disease epidemic patterns is analyzed in a single and multiple patch system connected by dispersal. Interaction of this sort between patches can disrupt the initial one patch disease dynamics; for example dispersal can cause a disease-free equilibrium where otherwise there would be none.

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Gerardo Chowell, Universidad de Colima
Sara Del Valle, New Jersey Institute of Technology
Dulcie Kermah, Howard University
Leisis Martino, Barry University
Project supervisor: Juan Pablo Aparicio, Cornell University