Markov semigroup approach to the analysis of a nonlinear stochastic plant disease model

In this article, we consider a stochastic plant disease model with logistic growth and saturated incidence rate. We analyze long-term behaviors of densities of the distributions of the solution. On the basis of the theory of Markov semigroup, we obtain the existence of asymptotically stable stationary distribution density of the stochastic system. We demonstrate that the densities can converge in L^1 to an invariant density under appropriate conditions. Moreover, we obtain the sufficient conditions for extinction of the disease. Also, we present a series of numerical simulations to illustrate our theoretical results.