Study On Several Virus Dynamic Models With Uncertain Factors

In recent years,considering the impact of environmental uncertainties on the replica-tion and value-added of viruses in vivo,many scholars have proposed some virus dynam-ics models with random disturbances,and obtained many important theoretical results.This thesis takes viruses as a research background,the impacts of random disturbance on the persistence and extinction of the virus are discussed.The main content of the study can be summarized as follows:1.In the first part(corresponding to the second section),a virus dynamics model with interference of uncertain factors is proposed,and the existence and uniqueness of the global positive solution of this model are proved.By constructing appropriate Lyapunov function,the criteria of virus extinction and endurance are established.The theoretical results show that uncertain factors have a certain inhibitory effect on the virus.When the intensity of the interference is large,it can promote the elimination of the virus.2.In the second part(corresponding to the third section),a stochastic HIV model with state transition and logistic growth is proposed.By constructing some Lyapunov functions with state transition,the unique ergodic stationary distribution of the model is obtained.Further,some sufficient conditions for the extinction of infected cells and free viruses are established.It is also proved that the susceptible cells have a unique ergodic stable distribution.Finally,the results of this paper are verified by numerical simulation.Theoretical analysis and numerical simulation show that,in a finite state space,low-intensity white noise can maintain the persistence of the virus,while high-intensity white noise can make the virus extinct after a period of time.3.In the third part(corresponding to the fourth section),a stochastic virus infection model with nonlinear incidence and intracellular delay is proposed,the existence of the only positive solution of the model is discussed.Further,the application of the Lyapunov function and the comparison principle of stochastic differential equations,Markov chain ergodicity,random integration and other analytical techniques,we proved that the solution of the model is normal and ergodic,and discussed the effect of white noise and telegraph noise on virus extinction.Finally,the theoretical results were verified with a numerical simulation.