Analysis On The Diffusive SIS Epidemic Model With Logistic Source

In this paper,two types of reaction-diffusion SIS with saturation incidence and logistic sources are considered in a spatially heterogeneous environment.Infectious disease model,in which the second model adds a spontaneous infection term to the first model.This paper first builds the dynamic behavior of the parabolic system,and next define the basic reproduction number of the systemR₀,where the selection ofR₀is related to the diffusion rate,whenR₀is less than 1,the DFE is linearly stable,and whenR₀is greater than 1,DFE is unstable and EE exists.Then the global stability of the positive solution is obtained.Further study the movement rates of susceptible and infected individuals tending to infinity or zero and the incidence of saturation tending to zero Asymptotic behavior of EE in poor size.Next consider an infectious disease with a spontaneous infection term based on this model model,first establish the consistent boundedness of the positive solution of the system,where the bound of the system(4-1)is obtained by using Moser-Alikakos Iterative method is established,and then the Lyapunov function is constructed to establish the global stability of the positive solution.Further research is easy to the effects of changes in the movement rate and saturation parameters of infected and infected individuals on the asymptotic behavior of EE were analyzed.The effect of each parameter change on the progressive behavior of the positive solution.From biological perspective,the above conclusions are important for preventing diseases.