Research On Age-structured Epidemic Models With Environmental Virus Infectious

In recent years,infectious diseases caused by viruses have become more and more frequent,causing serious harm to human survival and economic development.Take COVID-19 caused by SARS-Co V-2 as an example.Globally,as of 24 September 2020,there have been more than 100 million confirmed cases and 2965707 people have died.Therefore,understanding the spread of infectious diseases is extremely important for prevention and control of infectious diseases.In this paper,we study the dynamic behavior of age-dependent environmental viral epidemic models.Main contents of this paper described as follows:1.In the first part(chapter 2),an age-structured model for coupling withinhost and between-host dynamics in environmentally-driven infectious diseases is established.The positivity and ultimate boundedness of the solution,the basic reproduction number,the existence and the local asymptotic stability of the equilibria are obtained for the fast system of virus infection in the host and the slow system of disease transmission between the host.For the fast time system,the global asymptotic stability of the equilibria is obtained by using the Lyapunov function method.For isolated slow time system,we only obtain the global asymptotic stability of the disease-free equilibrium.For coupled slow time system,the dynamic behavior is complex and backward branching may occur.Finally,a numerical example is given to verify the rationality of the main conclusions.2.In the second part(chapter 3),an age-dependent SIER infectious disease model with environmental virus infection is established.Firstly,the basic theory of differential equation,comparison principle and asymptotic smoothness theory are used to obtain the positivity,boundedness and asymptotic smoothness of the solution.Secondly,the threshold condition for the existence of the equilibria of the model is established by the basic reproduction number.The local asymptotic stability of the equilibria is obtained by linearization method.The global asymptotic stability of the disease-free equilibrium of the model is obtained by the comparison principle;the uniform persistence of the disease is obtained by the dynamic system persistence theory of differential equations.At last,a numerical example is given to verify the rationality of the main conclusions and the correctness of the conjecture.