Analysis Of Vector-borne Epidemic Models With Age-structure And Random Disturbance

Age structure,including infection age,incubation age,immune age and so on,are all important factors affecting the transmission of vector borne diseases.In addition,environmental fluctuations also have a significant impact on the transmission of vector borne diseases.Based on this,this paper introduces age structure and random distur-bance into the model of vector borne diseases,discusses the existence and stability of various equilibrium states of the model,the persistence and extinction of the disease,The main contents can be summarized as follows:1.In the first part(corresponding to the second section),a vector infections dis-ease model with immune age,incubation period and general incidence is established.The existence,local stability,consistent persistence and asymptotic smoothness of the disease-free equilibrium state and endemic equilibrium state of the model are discussed.By applying the fluctuation principle and constructing appropriate Lyapunov function-al,the global asymptotic stability of all kinds of equilibrium states is obtained,The main theoretical results are verified by numerical simulation and the influence of age-dependent parameters on disease transmission is discussed.2.The second part(corresponding to the third section),considering that there is still the possibility of recurrence in the recovered population,and the recurrence rate will change with the increase of recovery time,a vector infectious disease model with age-dependent immunity and recurrence is established.The existence and local stabil-ity of various equilibrium states of the model,as well as the uniform weak persistence and asymptotic smoothness of the model solution are discussed.Furthermore,by con-structing Lyapunov functional,The global asymptotic stability of the equilibrium state is obtained.In addition,the optimal control problem is also discussed,and the optimal control conditions are obtained.The above results are verified by numerical model.3.The third part(corresponding to the fourth section),considering the impact of environmental fluctuations on infectious diseases and the existence of asymptomatic infection,a SIS epidemic model with random interference and asymptomatic infection is introduced.The existence and uniqueness of the positive solution and the random persistence and extinction of the disease are studied.More specifically,if R0<1,then the disease is extinct with probability 1;if R0>1,then disease is probable in the mean sense with probability 1.