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Stochastic Simulations of a Saptial SIR Model

In this paper we consider a stochastic spatial SIR (Susceptible-Infectious-Recovered) model. We assume that the population is distributed in separate cells. The disease is transmitted within the cell by direct contact, and from cell to cell through an external object (vector or vehicle) capable of carrying the disease. We simulate this model in a 10 x 10 grid of cells, and investigate the effects of the relative rates of transmission within and between cells on the predictability and progression of the disease. Results of simulation indicate that as the rate of intercellular transmission increases relative to intracellular transmission, the mean number becoming effected within each cell increases but so does the spatial variability. We also found that the time for the epidemic to run its course reaches a maximum average value at intermediate relative as does the spatial variability.

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Judit Camacho, University of California-Santa Cruz
Fernando Carreón, University of Texas-El Paso
Derik Castillo-Guajardo, Universidad Autónoma Metropolitana Unidad Xochimilco
Hugo Jiménez-Perez, Universidad Nacional Autónoma de México
Leticia Montoya-Gallardo, Universidad Nacional Autónoma de México
Ricardo Alberto Sáenz, University of Texas-El Paso