Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease

Abstract

This paper is concerned with a stochastic two-species competition model under the effect of disease. It is assumed that one of the competing populations is vulnerable to an infections disease. By the comparison theorem of stochastic differential equations, we prove the existence and uniqueness of global positive solution of the model. Then, the asymptotic pathwise behavior of the model is given via the exponential martingale inequality and Borel-Cantelli lemma. Next, we find a new method to prove the boundedness of the pth moment of the global positive solution. Then, sufficient conditions for extinction and persistence in mean are obtained. Furthermore, by constructing a suitable Lyapunov function, we investigate the asymptotic behavior of the stochastic model around the interior equilibrium of the deterministic model. At last, some numerical simulations are introduced to justify the analytical results. The results in this paper extend the previous related results.