Study On The Qualitative Properties Of A Reaction-Diffusion SIS Epidemic Mode

With the rapid development of the global economy,health issues are becoming more and more important to human beings,and the primary natural enemy of human health is infectious diseases,so it is important to study the transmission and prevention of infectious diseases.It is well known that there are many factors affecting the spread of infectious diseases,such as time,space,infection mechanism,spread rate of infected population,population density,mobility and so on.From an epidemiological point of view,mathematical modeling is an important tool to analyze the prevention of disease transmission.In this dissertation,we investigate a reaction-diffusion SIS infectious disease model with a Logistic growth term and a vector infection mechanism in a spatially heterogeneous setting,considering the potential applications of overcrowding in disease control and prevention.Firstly,the model is analyzed in a suitable way to derive the basic reproduction number of the model,and the relationship between the basic reproduction number and the principal eigenvalues and the rate of disease spread is discussed.Subsequently,the stability of the disease-free equilibrium and the consistent persistence of the system with respect to the basic reproduction number are analyzed.In particular,in the spatially homogeneous case,the Lyapunov functional is constructed to prove the global attractiveness of the unique constant endemic equilibrium.Finally,the asymptotic profiles of the endemic equilibrium is further explored when the human diffusion rate tends to zero or infinity.This dissertation finds that in the current model the disease will persist regardless of whether we control the spread rate of susceptible individuals.When we control for the rate of spread of infected individuals,the effect will be different under certain conditions depending on the risk area.In areas similar to low-risk areas,if we control the flow of infected individuals,the spread of the disease will be inhibited;in high-risk areas,the disease will persist.These provide useful insights into the impact of spatial heterogeneity and spatial dispersal rates on disease transmission and control.