The Analysis Of Virus Model And Population Model With Stochastic Perturbation

In recent years,the research on dynamically behaviour of biological mathematic-s with stochastic perturbation model has been widespread attention to domestic and international scholars.Our paper has launched a detailed research about the stochas-tic HBV infection model with nonlinear incidence rate and discussed dynamics of two predator-prey model with stochastic perturbation.Its main contents can be summarized as follows:1.In the first part,we propose a amended Hepatitis B virus model with stochastic perturbation and nonlinear incidence rate.By qualitative analysis of Lyapunov,com-parison principe of stochastic differential equations,integral and differential inequalities,Fokker-Planck equation,and some of analytical skills investigate the long time behavior of this stochastic model.First,if the basic infection reproductive number of the corre-sponding deterministic model is less than 1,some sufficient conditions for almost surely exponentially stable in the sense of the infected cells and free virus are established,and the stationary probability density function of the uninfected sell is also obtained.Further,we prove that the solution of this model has ergodic property under some conditions,and converges to the unique stationary distribution if the basic infection reproductive number is more than 1.In addition,we approximate the oscillatory behavior of this model about the two steady state of the corresponding deterministic model.Finally,the presented results are demonstrated by numerical simulations.2.In the second part,we propose a stochastic Lotka-Volterra model with seasonal variation and outside food resource,and the existence of global positive solution and boundedness are derived.Furthermore,we get some sufficient conditions for extinction,strong persistence in the mean and persistence in the sense of populations,respectively.In addition,by constructing some suitable Lyapunov functions,we show that there is at least one periodic solution and analyzed the relation between the species densities and intensities of white noises.Finally,the global attractiveness of solution of this model is discussed.3.In the third part,we propose and analysis,in this paper,a single predator mul-tiple prey stochastic model with seasonal variation.By using the method of solving an explicit solution,the existence of global positive solution of this model are obtained.The method is more convenient than Lyapunov analysis method for some population models.Moreover,the stochastically ultimate boundedness are considered by using the comparison theorem of stochastic differential equation.Further,some sufficient condi-tions for the extinction,strong persistence in the mean and the persistent in the sense of populations are discussed,respectively.In addition,by constructing some suitable Lyapunov functions,we show that this model admits at least one periodic solution and the globally attractivity of any solution.Finally,numerical simulations clearly illustrate the main theoretical results and the effects of white noise and seasonal variation for the persistence and extinction of populations.