Asymptotic Behavior Of Population And Epidemic Models Under Stochastic Environment

The asymptotic behavior of the species population system and epidemic model under stochastic environment has been studied in this paper.It's mainly divided into the following three parts.The first part of the study is non-autonomous stochastic model with pulse toxicant input and perturbation.We prove the existence and uniqueness of the periodical solution and it is globally attractivity with probability 1.The mean boundedness of solution is proved by constructing the comparison system and the sufficient conditions for persistence in the mean and non-persistence in the mean of the population is obtained.Finally,numerical simulations are presented to illustrate the effectiveness of our results.Secondly,a stochastic delayed predator-prey model driven by L?evy jumps is discussed.We prove the existence and stochastically ultimately boundedness of the global positive solution by using It?o formula.And the the sufficient conditions for persistence in the mean and extinction of the population are obtained.Furthermore we discuss the influence of the white noise and L?evy jumps,and show the persistence in the mean and extinction for the special case of the considered system.Finally,numerical simulations are presented to illustrate the effectiveness of our results.Thirdly,a stochastic SIRS model under Markov regime switching is proposed and investigated.We prove the existence of the global positive solution by using It?o formula.The sufficient conditions for the extinction of the epidemic are obtained.And we discuss the fluctuation near the equilibrium of the corresponding deterministic model.Finally,we give the numerical simulations to illustrate the effectiveness of our results.