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

Date

2019-10-18

Authors

Qi, Haokun
Meng, Xinzhu
Chang, Zhengbo

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

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 L1 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.

Description

Keywords

Plant disease model, Markov semigroup, Stationary distribution, Extinction

Citation

Qi, H., Meng, X., & Chang, Z. (2019). Markov semigroup approach to the analysis of a nonlinear stochastic plant disease model. <i>Electronic Journal of Differential Equations, 2019</i>(116), pp. 1-19.

Rights

Attribution 4.0 International

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