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ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE

Acta Mathematica Scientia 2003年第4期23卷 440-446页

作者：陆忠华 *** 高淑京 *** 陈兰荪 *** Supercomputing Center of Computer Network Information Center Chinese Academy of Sciences Beijing 100080 China E-mail:zhlu Department of Mathematics Guangzhou University Guangzhou 510405 China E-mail:gaosjmath Institute of Mathematics Academy of Mathematics & System Sciences Academia Sinica Beijing 100080 China E-mail:lschen

A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are in... 详细信息

关键词： SI epidemic model threshold disease free equilibrium endemic equilibrium global attractor

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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.

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Global Asymptotic Stability of a Kind of Stochastic SIRS Model

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Journal of Donghua University(English Edition) 2010年第6期27卷 792-795页

作者：徐敏丁永生胡良剑 Business Information Management School Shanghai Institute of Foreign Trade College of Information Science and Technology Donghua University College of Science Donghua University

A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)*** model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population *** making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was *** this condition,the epidemics will die out as time goes *** on this,almost surely exponential stability was analyzed.

关键词： stochastic SIRS model disease free equilibrium global asymptotic stability

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Stability Analysis of Bubonic Plague Model with the Causing Pathogen Yersinia pestis in the Environment

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Advances in Infectious diseases 2016年第3期6卷 120-137页

作者： Rigobert Charles Ngeleja Livingstone Luboobi Yaw Nkansah-Gyekye School of Computational and Communication Science and Engineering Nelson Mandela African Institution of Science and Technology Arusha Tanzania Department of Mathematics Makerere University Kampala Uganda

Bubonic plague is a serious bacterial disease, mainly transmitted to human beings and rodents through flea bite. However, the disease may also be transmitted upon the interaction with the infected materials or surfaces in the environment. In this study, a deterministic model for bubonic plague disease with Yersinia pestis in the environment is developed and analyzed. Conditions for existence and stability of the equilibrium points are established. Using Jacobian method disease free equilibrium (DFE) point, E0 was proved to be locally asymptotically stable. The Metzler matrix method was used to prove that the DFE was globally asymptotically stable when R0 equilibrium point of system is globally asymptotically stable when R0 > 1. Numerical simulations are done to verify the analytical predictions. The results show that bubonic plague can effectively be controlled or even be eradicated if efforts are made to ensure that there are effective and timely control strategies.

关键词： disease free equilibrium Endemic equilibrium Stability Analysis Bubonic Plague Pathogens in the Environment

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