The limit behavior of SEIRS model in spatial grid

Abstract

In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers.