Stability Study Of Heterogeneous Epidemiological Models

Infectious diseases are posing a serious threat to our health and safety.The prevention and treatment of infectious diseases is the focus of our attention,it is also the top priority for the government and the medical sector.Therefore,it's a meaningful topic to analyze how the factors(such as transmission routes,ways of infection etc)affect the disease transmission from the perspective of establishing epidemic models.It has both theoretical and practical significance.The contents of this paper are designed as follows:(1)We establish a virus infection model with latency and age-struture.We study the local asymptotic stability of the model by using the linearization method.The Lyapunov functional is used to prove that the unique endemic equilibrium is globally asymptotically stable.(2)We formulate an age-structured SVEIR model with latency and vaccination,prove the existence of the equilibria,give the form of the basic reproduction number.Morever,we also prove that the semi-flow is asymptotically smooth and the system is uniformly persistent,the existence of the global attractor is also addressed.Similarly,by constructing the Lyapunov function we prove the stability of the equilibria.(3)We propose a multi-group agestructured SEIR epidemic model with both latency and relapse.The basic reproduction number is given by defining the spectral radius of the regenerated matrix.The asymptotic smoothness of the semi-flow,the consistent continuity of the system and the global stability of the equilibrium are also proved.By analyzing the global dynamic properties of the model,the Lyapunov functional construction method can be used to prove the stability of ODEs and PDEs models.The results of the global stability of the equilibrium state can also offer theoretical guidance for control strategies and disease prevention.