Analysis Of An Oncolytic Virus Therapy Model Solution With Immune Response

In this thesis,we consider an oncolytic virotherapy model with immune response.The existence and uniqueness of local solution and global solution of the model are discussed mainly by using Lp-theory,characteristic curve and the contraction mapping principle.The corresponding biological explanations are given in the end of this thesis.The main contents in the thesis are as follows:In Chapter 1,we elaborate the current medical status of tumor treatment,the application of partial differential equations in tumor treatment and the results achieved in recent years,analyze the importance of oncolytic virus therapy in tumor treatment,and introduce a oncolytic virotherapy model with immune response we will study,which is a kind of nonlinear free boundary problem.In Chapter 2,we transform the model to simplify the model.The free boundary problem is converted to an initial boundary value problem on the fixed boundary,we use characteristic curve to transform partial differential equations into ordinary differential equations,and the non-negative boundedness of the solution is obtained.Solve the 7 sets of constant equilibrium solutions of the model,and transform the model on this basis to study the stability of the constant equilibrium solutions.In Chapter 3,we discuss the existence and uniqueness of local solutions of the model after transformation.Under the given radial velocity,we analyze the model separately by using the Lp-theory and characteristic curve,and then apply contraction mapping principle to prove that the local solution of the model is unique.Meanwhile,we apply contraction mapping principle to prove that even if the radial velocity is uncertain,local solution of the model is also unique.In Chapter 4,we extend the local solution obtained in Chapter 3,and prove the existence and uniqueness of the global solution.It shows that the constant equilibrium solution of oncolytic virotherapy model is stable.Finally,the global solution of oncolytic virotherapy model with immune response is unique through the same method.Therefore,when the cell level in the tumor is controlled at a stable constant equilibrium solution,the tumor may eventually be cured by injecting a certain amount of virus.