Research On Vector-borne Epidemic Models With Stochastic Perturbation And Age-structure

Vector-borne diseases are caused by parasites,viruses and bacteria,which are transmitted by mosquitoes,sandflies and mice.They are one of the most common infectious diseases in the world.In recent years,many domestic and foreign scholars have established a large number of mathematical models to describe the transmission laws of various vector-borne diseases between hosts and vectors,and to seek the optimal strategy for disease prevention and control.A series of important research results have been obtained.Considering the important roles of vaccines in disease control,the age-structured phenomenon of host population and environmental noise in disease transmission.This thesis focuses on some classes of stochastic vector-borne disease models with agestructured and environmental noise interference.The main research contents include the following three aspects:In the first part(Corresponds to Chapter 3),a vector-borne disease dynamic model with white noise perturbation and immune age is established.By constructing suitable Lyapunov function,the existence and uniqueness of global positive solution of this model are obtained.The extinction of disease and stochastic stability of disease-free equilibrium are discussed.The criterion for the existence and uniqueness of ergodic stationary distribution of the model is established.Finally,some numerical simulations are carried to explain the theoretical results.In the second part(Corresponds to Chapter 4),the Markov transformation and Levy jump are introduced into a vector-borne disease model with white noise perturbation to discuss the above factors on the transmission and control of infectious diseases.Firstly,the existence of unique global positive solution of this model is proved by constructing suitable Lyapunov function.Furthermore,the sufficient conditions for the persistence and extinction of disease are obtained by using the strong number theorem.In the third part(Corresponds to Chapter 5),the optimal control problem of a stochastic vector-borne diseases model with Markov transformation and Levy jump is discussed.Taking the cost of treating diseases as the objective function,the sufficient conditions for the existence of near-optimal control of this model are established by using Hamiltonian function.