Study On The Dynamic Behavior Of The Brain Cancer Treatment Model With Impulsive Injection Of Zika Virus

Cerebral cancer is one of cancer that threatens the health of human.The prevention and treatment of cerebral cancer has always been one of the important subjects of scientists and medical staff.A new study suggested that Zika specifically kills stem cells in cerebral cancer,that it combines with conventional treatments may be an effective mean of treating deadly cerebral cancer which is also called plasmoblastoma.In this paper,we utilize the idea of biological mathematical modeling to establish the relevant mathematical model,according to the above research results.And then we qualitatively analyze the model.The main achievements are as follows:In chapter 2,with the idea of bio-mathematical modeling,we constructed a differential equation model for the treatment with cerebral cancer by impulsive injection of Zika.In the case of no impulsive injection of Zika,we analyzed the boundedness and nonnegativeness of the solutions of the model.And depending on the stability theory of ordinary differential equation,we explored the stability and threshold of the model equilibrium point.When considering the situation of impulsive injection of Zika,we discussed the local asymptotic stability of periodic solution under the impulsive condition by using the theory of impulsive differential equation.And we estimated impulsive injection volume and impulsive period length.Finally,we carried out the numerical simulation to explain the main conclusions of this thesis.In chapter 3,we analyzed the relationship between uninfected cerebral cancer cells,infected cerebral cancer cells and Zika virus,establishing the corresponding impulsive differential equation model.Then,we improved and analyzed the existing model.We got it from the research that when the period of the impulsive injection of Zika virus meets certain conditions,the periodic solution of the system is globally asymptotically stable.At this point,cerebral cancer is completely eliminated,consequently,the patient is curable.In addition,we also discussed the persistence and extinction of the system(3-3),and estimated the length of the impulsive period.We compared the situation of impulsive injection of Zika with that of continuous injection of Zika,and obtained the advantages of injection of Zika.Finally,we did some numerical simulations of the research result and made some summary.