The Law Of Large Numbers For The SEIRS Model Under A Spatial Grid

In this thesis,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 introduct the basic reproduction of this model.Then we consider the relation between the system of PDE and the discrete ODE model.Finally,due to the deterministic model ignores the impact of heterogeneity,thus we consider the stochastic model,and we prove two laws of large numbers.