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Long-Time Behavior of a Stochastic Turbidostat Model Under Degenerate Diffusion

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Journal of Systems Science & Complexity 2023年第4期36卷 1641-1657页

作者： CAO Zhongwei MU Xiaojie jiang daqing Center for Teaching Faculty Development Jilin University of Finance and EconomicsChangchun 130117China School of Petroleum Engineering Key Laboratory of Unconventional Oil&Gas DevelopmentChina University of Petroleum(East China)Ministry of EducationQingdao 266580China College of Science China University of Petroleum(East China)Qingdao 266580China

Due to many uncertain factors,parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental *** this paper,the authors develop a stochastic turbidostat model that considers white noise,formulate and analyze dynamical behavior for the stochastic *** authors obtain the existence and uniqueness of globally positive *** conditions of the extinction for the system are *** the uniformly elliptic condition can fail to satisfy,the existence of the stationary distribution of the system is proved by using Markov semigroups *** speaking,the existence of stationary distribution suggests that microorganism will exist for a long *** analytical results are tested and verified by numerical simulations,which evaluate the influence of white noise on the dynamics of microorganism.

关键词： Degenerate diffusion extinction markov semigroups stationary distribution stochastic turbidostat model

ANALYSIS OF A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY

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International Journal of Biomathematics 2013年第3期6卷 11-31页

作者： CHUNYANJI 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 130023 Jilin P. R. China School of Mathematics and Statistics Northeast Normal University Changchun 130024 Jilin P. R. China

In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equi- librium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.

关键词： Predator prey model with disease Ito formula stable stochastically unsta-ble stochastically stable in the large.

DYNAMICS OF AN HIV-1 INFECTION MODEL WITH CELL-MEDIATED IMMUNE RESPONSE AND STOCHASTIC PERTURBATION

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International Journal of Biomathematics 2012年第5期5卷 103-127页

作者： CHUNYAN JI daqing jiang School of Mathematics and Statistics Changshu Institute of TechnologyChangshu 215500 Jiangsu P. R. China School of Mathematics and Statistics Northeast Normal UniversityChangchun 130023 Jilin P. R. China School of Mathematics and Statistics Northeast Normal UniversityChangchun 130024 Jilin P. R. China

In this paper, we introduce the stochasticity into an HIV-1 infection model with cytotoxic T lymphocytes （CTLs） immune response via the technique of parameter perturbation. We show that there is a positive solution as desired in any population dynamics. Then we analyze the long time behavior of this model. We obtain a sufficient condition for the stochastic asymptotic stability in the large of the infection-free equilibrium and give the conditions for the solution fluctuating around the two infection equilibria （one without CTLs being activated and the other with）. Finally, we make sinmlations to conform to our analytical results.

关键词： HIV-1 infection the infection-free equilibrium the CTL^inactivated infectionequilibrium the interior equilibrium stochastic asymptotic stability in the large.

The asymptotic behavior of a stochastic multigroup SIS model

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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.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

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International Journal of Biomathematics 2021年第7期14卷 45-83页

作者： Qun Liu daqing jiang Key Laboratory of Applied Statistics of MOE School of Mathenatics and Statistics Northeast Normal University Changchun 130024Jilin ProvinceP.R.China College of Science China University of PetroleumQingdao 266580Shandong ProvinceP.R.China Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group King Abdulaziz University JeddahSaudi Arabia

In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence *** obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic *** addition,we make up adequate conditions for complete eradication and wip-ing out the infectious *** a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long ***,examples and numerical simulations are introduced to validate our theoretical results.

关键词： Multigroup HlV model staged progression saturated incidence rate station-ary distribution and ergodicity extinction

The asymptotic behavior and ergodicity of stochastically perturbed SVIR epidemic model

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International Journal of Biomathematics 2016年第3期9卷 177-190页

作者： Yanan Zhao daqing jiang School of Mathematics and Statistics Northeast Normal University Changchun 130024 Jilin P. R. China School of Science Changchun University Changchun 130022 Jilin P. R. China Nonlinear Analysis and Applied Mathematics (NAAM) Research Group King Abdulaziz University Jeddah Saudi Arabia College of Science China University of Petroleum (East China) Qingdao 266580 P. R. China

In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.

关键词： Stochastic SVIR epidemic model disease-free equilibrium stationary distri-bution ergodicity stochastic Lyapunov functions.

PERIODIC BOUNDARY VALUE PROBLEM OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH PERTURBATION

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Applied Mathematics(A Journal of Chinese Universities) 1999年第1期14卷 1-6页

作者： Liu Huizhao\ jiang daqing Dept. of Appl. Math. Hebei Univ. of Technology Tianjin Dept. of Math. Northeast Normal Univ. Changchun

Abstract By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation (t)=b(t,x t)+G(t,x t),\ 0≤t≤T, x(0)=x(T). is proved, where x(t) ∈R n,x t∈BC(R,R n) are given by x t(s)=x(t+s), b and G are continuous mappings from ×BC (R,R n ) into R n and take bounded sets into bounded sets, b(t,φ) is linear with respect to φ∈BC (R,R n ). Furthermore, a similar result to the periodic boundary value problem of functional differential equations with infinite delay is established.

关键词： 1991 MR Subject Classification 34B15

Stationary distribution and extinction for a stochastic two-compartment model of B-cell chronic lymphocytic leukemia

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International Journal of Biomathematics 2021年第8期14卷 141-156页

作者： Miaomiao Gao daqing jiang Xiangdan Wen College of Science China University of Petroleum(East China)Qingdao 266580P.R.China Key Laboratory of Unconventional Oil and Gas Development China University of Petroleum(East China)Ministry of EducationQingdao 266580P.R.China Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group Department of MathematicsKing Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics Yanbian UniversityYanji 133002Jilin ProvinceP.R.China

In this paper,we study the dynamical behavior of a stochastic two-compartment model of B-cell chronic lymphocytic leukemia,which is perturbed by white ***,by constructing suitable Lyapunov functions,we establish sufficient conditions for the existence of a unique ergodic stationary ***,conditions for extinction of the disease are ***,numerical simulations are presented for supporting the theoretical *** results show that large noise intensity may contribute to extinction of the disease.

关键词： Stochastic two-compartment model B-cell chronic lymphocytic leukemia stationary distribution extinction

Dynamics of a stochastic rabies epidemic model with Markovian switching

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International Journal of Biomathematics 2021年第5期14卷 163-198页

作者： Hao Peng Xinhong Zhang daqing jiang College of Science China University of Petroleum(East China)Qingdao 266580 P.R.China

In this paper,we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph ***,we prove the existence of the unique global positive ***,by constructing an appropriate Lyapunov function,we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the *** we establish sufficient conditions for the extinction of ***,numerical simulations are introduced to illustrate our theoretical results.

关键词： Stochastic rabies model stationary distribution Markovian chain extinction