Affiliation:
1. School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
2. International School of Public Health and One Health, Hainan Medical University, Haikou 571199, China
Abstract
<abstract><p>A stochastic Microcystins degradation model with distributed delay is studied in this paper. We first demonstrate the existence and uniqueness of a global positive solution to the stochastic system. Second, we derive a stochastic critical value $ R_0^s $ related to the basic reproduction number $ R_0 $. By constructing suitable Lyapunov function types, we obtain the existence of an ergodic stationary distribution of the stochastic system if $ R_0^s > 1. $ Next, by means of the method developed to solve the general four-dimensional Fokker-Planck equation, the exact expression of the probability density function of the stochastic model around the quasi-endemic equilibrium is derived, which is the key aim of the present paper. In the analysis of statistical significance, the explicit density function can reflect all dynamical properties of a chemostat model. To validate our theoretical conclusions, we present examples and numerical simulations.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine