Research Of Dynamic Behaviors Of A Class Of SIS Model

In the field of biomathematics,epidemic models have attracted wide attention and a large number of data have been obtained,which is of great significance to the study of infectious diseases.Aiming at the problem of infectious diseases,this paper studies the stability of disease-free equilibrium and the existence of endemic equilibrium using qualitative analysis and stability theory,implicit function existence theorem,eigenvalue theory,comparison principle and maximum principle.Specific research contents are as follows:First,The existence and uniqueness of disease-free equilibrium point are studied,and the basic regeneration number is characterized.The relationship between the stability of disease-free equilibrium point and the basic regeneration number is obtained.Secondly,It is proved that the equilibrium point of endemic diseases exists when the basic regeneration number is greater than 1,The nonexistence of the equilibrium point of endemic diseases was also discussed.Last,When the diffusion coefficients of susceptible and infected persons are equal,the stability of endemic equilibrium in high-risk areas and disease-free equilibrium in low-risk areas are proved.The above research results will help people to understand the transmission mechanism of diseases more clearly,thus laying a theoretical foundation for the prevention and treatment of infectious diseases.