Electron. J. Differential Equations,
Vol. 2019 (2019), No. 116, pp. 1-19.
Markov semigroup approach to the analysis of a nonlinear
stochastic plant disease model
Haokun Qi, Xinzhu Meng, Zhengbo Chang
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 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.
Submitted March 4, 2019. Published October 18, 2019.
Math Subject Classifications: 34D05, 60H10, 92B05.
Key Words: Plant disease model; Markov semigroup; stationary distribution;
extinction.
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Haokun Qi
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: haokun_2017@163.com
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Xinzhu Meng
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: mxz721106@sdust.edu.cn
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Zhengbo Chang
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: zbchang98@126.com
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