| Now,the virus has been a difficult problem for human beings to overcome.The rapid development of virus dynamics and infectious disease dynamics has become one of the most active fields in the field of cross study of biological mathematics.In particular,the study of the theory of random differential equations in the virus dynamics provides new ideas and methods for the evolution and treatment of the virus.In this paper,based on the virus model of the insoluble immune effect of the stochastic differential equation,the effects of random fluctuations on the extinction and persistence of the virus are systematically studied.The main contents and conclusions of this paper are showed as follows:Firstly,we study the effect of stochastic fluctuation on the virus infection model with nonlytic immune response.And we derive the expression of the regenerative number from the mathematical point of view,and analyze the stability of the disease-free equilibrium point and the disease equilibrium point.Then we have proved the virus extinction and the persistent threshold conditions by strict mathematical proof.In addition,the persistent upper and lower bounds of the virus have been obtained.The study found that noise plays a key role in the extinction and enduring of the virus,which provides a theoretical basis for further study of the virus infection model.Secondly,we study the dynamic of virus infection model with nonlytic immune response influenced by external fluctuation and periodic treatment.We describe the model of virus infection under periodic treatment,and obtain the threshold conditions for the virus extinction and weak persistence and the mean non persistent periodic treatment.In addition,making use of the methods of Ito’s formula and Lyapunov function,the threshold for extinction,weak persistence and non-persistent in the mean of virus is carried out by the strict mathematical proofs.As the intensity of periodic treatment increases,the virus presents a process from a weak persistence to a non lasting mean,and a final experience of extinction.At this point,periodic therapy can provide a good theoretical basis for the treatment of diseases.Thirdly,we investigates the dynamic of delayed virus infection model with nonlytic immune response influenced by external fluctuation.The mathematical model of virus evolution is established by the delay based stochastic differential equation under the influence of environmental noise.By using the Ito ’s formula and the Lyapunov function,the conditions for the extinction and weak persistence of the virus are obtained.It is concluded that the limit of the number of regenerative numbers in the delay sense is smaller than the regenerative number of the deterministic.On the most important point,the balance point can be changed by changing the length of the immune cycle,which provides a better theoretical basis for our treatment of disease. |
