Dynamic Modeling And Analyzing On Two Classes Of Mosquito-Borne Infectious Diseases With Repeated Infection

Infectious diseases are caused by a variety of pathogens that can be transmitted from human to human,animal to animal,or human to animal.Its spread and prevalence not only affect the socio-economic development,but also threaten the life and health of human beings.The COVID-19 outbreak reminds people again of the importance of the prevention and control of infectious diseases.The prevention and control of infectious diseases cannot be separated from the scientific understanding of their epidemic law and transmission characteristics.Mathematical modeling research has become an important tool to predict and control infectious diseases.Based on the characteristics of infection and transmission of mosquito-borne diseases such as malaria and dengue fever,in this paper,we establish and analyze the dynamic models of two classes of mosquito-borne infectious diseases with repeated infection by using the theories and methods of age-structured infectious disease dynamics and time-delay differential system.The main research contents are as follows:Firstly,a model of mosquito-borne infectious disease dynamics with age structure and repeated infection is proposed and analyzed,based on the characteristics that children are susceptible to malaria transmission,while the adult population has acquired strong immunity through multiple infections and vaccination helps to resist infection.In the model analysis,we give the expression of the basic reproduction number of the system by applying the basic reproduction number theory.Using theories and methods such as linear characteristic equation characterization and stability,we prove the global stability of the disease-free equilibrium states and obtain the existence conditions of multiple endemic equilibrium states in the system.The Lyapunov-Schmidt theory and method are applied to show the existence of backward bifurcation of the system.And using the theory and method of continuous survival of infinite-dimensional dynamical systems,we give proof of the uniform strong persistence of diseases in the system.The biological interpretations of the results in the model are also given.Secondly,based on the characteristics of asymptomatic infection in mosquitoborne infectious diseases such as malaria and dengue fever,and a period of complete immune protection after infection recovery,we model a class of mosquito-borne infectious diseases with asymptomatic and repeated infection,and analyze the effect of asymptomatic infection and immune protection on the development of mosquitoborne diseases.In model analysis,the positivity and boundedness of the solution of the system are analyzed.Using methods such as the next generation matrix theory of infectious diseases,we give the expression of the basic reproduction number and prove the local stability of the uninfected equilibrium state of the system.The existence of all positive equilibrium states and the conditions for backward branching of the system are given using methods such as Descartes Rule of Signs and Central Manifold Theorem.Finally,applying and developing the theory and method of Pontryagin’s Minimum Value Principle with time delay,we give the optimal control strategy for the constructed system.Also,we explain the biological implications revealed by the model.