Dynamic Analysis Of An Oncolytic Virus Therapy Model With Age Structure

Oncolytic viral therapies are new and promising approaches to cancer treatment.Considering that the growth rate,death rate,etc.of infected cells vary with their lifespan,the age structure model of virus infection has attracted much attention from researchers.In this thesis,three oncolytic virus therapy models with age structure are established and studied.In Chapter 3,considering that the growth rate and death rate of infected tumor cells change with the change of their life span,an oncolytic therapy model with age structure is established to analyze the infuence of the age of infected tumor cells on oncolytic virus treatment of cancer.Using the theory of linear operator semigroup,the model to be studied is expressed as a non-uniform Cauchy problem.The existence,uniqueness,point dissipation and asymptotic smoothness of the strong continuous semi-fow of the system are studied,and the existence theorem of the global compact attractor of the system is obtained.According to the results obtained after the linearization of the system,the expressions of the equilibrium solution and the basic reproduction number are given.Volterra formula is used to transform the model to an ordinary diferential equation system,and the stability of the equilibrium solution is proved by the Jacobian matrix and Lyapunov function.The relationship between the global asymptotic stability and the basic reproduction number of the infection-free steady state and the infection-infected steady state of the model is analyzed.The conclusion is verifed by numerical simulation.In Chapter 4,considering the combination of injected oncolytic virus and modifed oncolytic virus,Holling-Ⅱ reaction function is used to describe the saturation efect between uninfected tumor cells and virions,and an age-structured oncolytic therapy model with saturation efect is established.Firstly,by studying the bounded dissipation and asymptotic smoothness of the semi-fow of the system,the existence and uniqueness of the global positive solution of the system are proved.Secondly,the basic reproduction number of the system and the threshold for the existence of the steady state are obtained according to the equations satisfed by the infected steady state.Then,the Jacobian matrix is used to analyze the local stability of the infection-free steady state of the system.The global stability of the infection-free steady state was analyzed by updating the integral equation.The local stability of the infected steady state is established by analyzing the linearized system.Suffcient conditions for the global stability of the infected steady state are obtained by constructing Lyapunov functions.Finally,the theoretical analysis was verifed by numerical simulation,and the feasibility of oncolytic virus in cancer treatment was discussed and summarized in combination with biological signifcance.In Chapter 5,based on the deterministic model studied in chapter 4,white noise is introduced to consider the continuous small random disturbance in the tumor microenvironment.Considering the infuence of random factors and age structure on oncolytic virus treatment of cancer,an age structure stochastic diferential equation model is established.Gronwall inequality is used to prove that a positive solution to the model exists and is unique.By using Jensen’s inequality,Ito’s formula and inequality analysis techniques,suffcient conditions for the extinction and persistence of the system are obtained.