Study On Vector-borne Epidemic Models With Class-age Structure

In recent years,considering the class-age structure,such as the age of infection,the age of incubation,and the influence of time delay on vector-borne diseases,many scholars at home and abroad have carried out a series of studies on this issue and obtained many important results.This thesis introduces class-age structure and latency into the vector-borne disease model to discuss the existence and stability of various equilibrium states of the model species,as well as the consistent persistence of the disease.The main contents can be summarized as follows:1.In the first part(corresponding to the second quarter),a vector infectious disease model with incubation age and horizontal transmission is established.The existence and local stability of the disease-free equilibrium and the endemic equilibrium state as well as the uniform persistence of model solution are studied.By constructing proper Lyapunov functionals,the global asymptotic stability of the equilibrium states is obtained.Finally,the main theoretical results are verified by numerical simulation.2.In the second part(corresponding to the third quarter),a model of vectorborne diseases with age-dependent immunity and latency is proposed.The existence and local stability of the equilibrium state,uniform persistence of the model solution are discussed.Furthermore,the global asymptotic stability of the equilibrium state is obtained by constructing the Lyapunov functional.In addition,the optimal control problem is discussed and the optimal control conditions are obtained.Finally,the numerical model is used to verify the above results.3.In the third part(corresponding to the forth quarter),taking into account the incubation period of the virus in the vector,an infectious disease model with latency age of host and vector is proposed.The existence and uniqueness of the equilibrium states of the model are proved by using Lyapunov function and differential equation theory,and the local and global stability of various equilibrium states are obtained.The main theoretical results are explained by numerical simulation.