Behavior of an Epidemic Model of Ecologically Transmissible Diseases with Nonlinear Incidence

张少辉; 靳祯

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Behavior of an Epidemic Model of Ecologically Transmissible Diseases with Nonlinear Incidence

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- Behavior of an Epidemic Model of Ecologically Transmissible Diseases with Nonlinear Incidence
- 具有非线性发生率的传染病模型性态分析
- Vol. 33, Issue 4, Pages: 353-357(2012)
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
- DOI：
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- Published：2012
- 稿件说明：
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张少辉, 靳祯. Behavior of an Epidemic Model of Ecologically Transmissible Diseases with Nonlinear Incidence[J]. 2012, 33(4): 353-357.
DOI：

张少辉, 靳祯. Behavior of an Epidemic Model of Ecologically Transmissible Diseases with Nonlinear Incidence[J]. 2012, 33(4): 353-357. DOI：

摘要

研究了具有非线性发生率的SIR传染病模型.该发生率满足一定条件.通过对模型的分析

发现模型参数在满足某些值时

模型会发生后向分支现象.此时R0=1不能作为疾病是否消亡的阈值条件.在拐点处的临界值被作为新的阈值.分析了模型发生后向分支的条件

得到了无病平衡点和地方病平衡点稳定的充分条件.主要结论均通过数值模拟加以验证.

Abstract

An SIR epidemic model with non-linear incidence rate which subject to a few general conditions is investigated.It is found that the backfoward bifurcation occurs for the model if some parameters are specific values.To drive the basic reproduction number less than the unity is not enough to eradicate the disease

and the critical value at the turning point becomes a new threshold.Some sufficient conditions for the disease-free equilibrium and the endemic equilibrium being stable are also obtained.The main results are illustrated by numerical simulations.

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references

Murray J D.Mathematical Biology[M].2nd ed.Beijing:Springer Overlag,1998.

Hethcote H W.The mathematics of infectious disease[J].SIAM Rev.,2000,42:599-653.

Capasso V,Serio G.A generalization of the Kermack-McKendrick deterministic epidemic model[J].Math.Biosci,1978,42:43-61.

Liu W M,Hethcote H W,Levin S A.Dynamical behavior of epidemiological models with nonlinear incidence rates[J].J.Math.Biol.,1987,25:359-380.

Liu W M,Levin S A,Iwasa Y.Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models[J].J.Math.Biol,1986,23:187-204.

Ruana Shigui,Wang Wendi.Dynamical behavior of an epidemic model with a nonlinear incidence rate[J].Journal of Differential Equations,2003,188:135-163.

Zhou Yugui,Xiao Dongmei,Li Yilong.Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action[J].Chaos,Solitons and Fractals,2007,32:1903-1915.

Alexander M E,Moghadas S M.Periodicity in an epidemic model with a generalized non-linear incidence[J].Mathematical Biosciences,2004,189:75-96.

Kupiec P.Techniques for verifying the accuracy of risk measurement models[J].Journal of Derivatives,1995,3:73-84.

Zhang Xu,Liu Xianning.Backward bifurcation of an epidemic model with saturated treatment function[J].J.Math.Anal.Appl,2008,348:433-443.

Hu Zhixing,Liu Sheng,Wang Hui.Backward bifurcation of an epidemic model with standard incidence rate and treatment rate[J].Nonlinear Analysis:Real World Applications,2008,9:2302-2312.

Cui Jingan,Mu Xiaoxia,Wan Hui.Saturation recovery leads to multiple endemic equilibria and backward bifurcation[J].Journal of Theoretical Biology,2008,254:275-283.

Wang Wendi.Backward bifurcation of an epidemic model with treatment[J].Mathematical Biosciences,2006,201:58-71.

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