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An sis epidemic model with diffusion

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Applied Mathematics(A Journal of Chinese Universities) 2017年第2期32卷 127-146页

作者： XU Zhi-ting CHEN Dan-xia School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China.

The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an sis epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.

关键词： sis epidemic model traveling wave solution local stability global stability diffusive.

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Analysis of a sis epidemic model with stage structure and a delay

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Communications in Nonlinear Science and Numerical Simulation 2001年第1期6卷 35-39页

作者： Yanni XIAO and Lansun CHEN (Academy of Mathematics & System Sciences, Academic Sinica, Beijing 100080, China ) Academy of Mathematics & System Sciences Academia Sinica Beijing 100080 China

A disease transmission model of sis type with Stage structure and a delay corresponding to the infectious period is formulated. By constructing the difference operator and using global convergence theorem, we show that the disease-free equilibrium is globally asymp- totically stable. The Stability of an endemic equilibrium are investigated for the differential- difference equations.

关键词： sis epidemic model delay threshold globally asymptotically stable

Dynamical analysis of an sis epidemic model with migration and residence time

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International Journal of Biomathematics 2021年第4期14卷 141-158页

作者： Maoxing Liu Xinjie Fu Donghua Zhao Department of Mathematics North University of China TaiyuanShanxiP.R.China School of Mathematical Science Fudan University Shanghai 200433P.R.China

Migration can be ciivided into temporary and permanent migration,which is related to the residence time of people in the patch,thus we consider an sis epidemic model with migration and residence time in a patchy environment.If R0≤1,the disease-free equilibrium is globally asymptotically stable and the disease dies out.With the same migration rate of susceptible and infectious individuals and without disease-induced death,when R0>1,the endemic equilibrium is unique and globally asymptotically stable.Numerical simulations are carried out to show the effects of residence time and the migration rate on disease prevalence.

关键词： sis epidemic model patchy environment migration residence time Lyapunov function global stability

An sis epidemic model with Stage Structure and a Delay

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 607-618页

作者： Yan-ni Xiao, Lan-sun ChenAcademy of Mathematics and System Sciences, Chinese Academy of Sciences. Beijing 100080. China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

A disease transmission model of sis type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.

关键词： sis epidemic model threshold globally asymptotically stable hopf bifurcation stage structure

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A stochastic epidemic model on homogeneous networks

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Chinese Physics B 2009年第12期18卷 5111-5116页

作者：刘茂省阮炯 Department of Mathematics North University of China School of Mathematical Sciences Fudan University

In this paper, a stochastic sis epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R^＊, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 〉1, the epidemic will die out as long as noise intensity satisfies a certain condition.

关键词： homogeneous networks sis epidemic model stochastic stability stochastic bifurcation

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Global Stability of the Deterministic and Stochastic sis epidemic models with Vaccination

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Journal of Mathematical Research with Applications 2021年第1期41卷 62-68页

作者： Xu ZHAO Wenshu ZHOU School of Mathematics and Information Science Beifang Minzu University School of Science Dalian Minzu University

We study the stability of endemic equilibriums of the deterministic and stochastic sis epidemic models with vaccination. The deterministic sis epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.

关键词： sis epidemic model vaccination global stability