Dynamic Properties Of The Tumor-immune Reaction Diffusion Model With Time Dela

Cancer has brought serious harm to human life and social economic development,so it is necessary to study the law of development of this kind of disease.In recent years,the research on tumor cell model has become a hot topic in biomathematics research.Based on this,this thesis studies the dynamic properties of two tumor therapeutic models.First,a reaction-diffusion model of oncolytic virus therapy with delay was established.The nonexistence of steady-state solution,steady-state solution stability and the existence of Hopf bifurcation of the model are discussed,and corresponding numerical examples are given.From the overall perspective of the model,in order to make oncolytic virus kill tumor cells more effectively,oncolytic virus should be designed with low toxicity,short virus life cycle,rapid replication and good virus-specific immune evasion ability.Studies have shown that the reaction-diffusion model of oncolytic virus therapy with time delay produces more complex dynamic properties.Secondly,a tumor-immune response diffusion model with time delay is established.The existence and stability of steady-state solutions are discussed,the existence and properties of Hopf bifurcation are analyzed,and some numerical examples are given.It can be concluded that the stability of the system will change by adding time delay.It can be found that without time delay,if tumor cells grow slowly before and at the moment of mitosis and reach a state of equilibrium under the action of immune cells,but the introduction of a larger time delay makes the equilibrium state become unstable,and the number of cells will oscillate periodically.The results of stability analysis show that time delay is the main reason for generating oscillatory periodic solutions.