Stability Analysis of SEIS model with spatial variations

Abstract

In this report we present an SEIS model for infectious diseases with latent period and no immune response for spatially heterogeneous environment. Spatial heterogeneity is designed by several metapopulations. It was shown that global dynamics of an epidemics completely depends on basic reproduction number R0. By fxing the number of patches to two, we use next generation matrix method to obtain basic reproduction number and make further analysis on it. Migration rates of individuals are considered as one of the main factors that influence R0. Moreover, some numerical simulations for the dynamics of the system with different initial conditions is presented.