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