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The asymptotic behavior of a stochastic multigroup SIS model

International Journal of Biomathematics 2018年第3期11卷 115-130页

作者： Chunyan Ji Daqing Jiang School of Mathematics and Statistics Changshu Institute of Technology Changshu 215500 Jiangsu P. R. China School of Mathematics and Statistics Northeast Normal University Changchun 130024 Jilin P. R. China College of Science China University of Petroleum (East China) Qingdao 266580 P. R. China Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group King Abdulaziz University Jeddah Saudi Arabia

In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution.under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

关键词： A multigroup Susceptible-Infected-Susceptible (SIS) model disease free equilibrium endemic equilibrium exponential stability prevail stationary distribution.

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Analysis of a stochastic model for algal bloom with nutrient recycling

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International Journal of Biomathematics 2016年第6期9卷 59-85页

作者： Xuehui Ji Sanling Yuan Huaiping Zhu School of ManagementUniversity of Shanghai for Science and Technology Shanghai 200093 P. R. China College of ScienceUniversity of Shanghai for Science and Technology Shanghai 200093 P. R. China Department of Mathematics and StatisticsYork University Toronto M3J 1P3 Canada

In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.

关键词： Stochastic nutrient-algae model ItS's formula stochastic stability integralMarkov semigroup stationary distribution.

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