The Analysis Of Diffused SI Model With Constant Input Rate And Non-linear Transmission Rate

Diffused with constant rate and non-linear transmission rateβIp Sq of the SI model is constructed for a non-linear population dynamics and the transmission rate of infec-tious disease model study. Previous non-linear model of the transmission rate of infec-tious disease use stability theory of ordinary differential equations model analysis of the existence of equilibrium and stability,and the use of partial differential equations of the model theory in Dirichlet boundary conditions and Neumann boundary conditions analysis of the model under the existence of equilibrium and stability. In this paper,we conclude the equilibrium point to eliminate diseases and endemic diseases of the exis-tence of equilibrium and stability.There are four chapters in this thesis.In Chapter 1, we introduce the research background of infectious diseases,given of the concept of infectious diseases.model and research significance. And the conclusion using ordinary differential equations study by predecessors.In Chapter 2, we firstly introduce the needed theorems, and then study the existence of equilibrium solution of the model under the conditions of Dirichlet in two ways.In Chapter 3, we firstly introduce the needed theorems,and then study the stability of equilibrium solution of the model under the conditions of Neumann.In Chapter 4, the main conclusions of this thesis are summarized.It gives the latest research results and the further research prospect.