王世飞, 王娟, 王海霞. 具有接种疫苗年龄结构的SIRS流行病模型分析[J]. 信阳师范学院学报(自然科学版), 2007, 20(4): 395-398.
引用本文: 王世飞, 王娟, 王海霞. 具有接种疫苗年龄结构的SIRS流行病模型分析[J]. 信阳师范学院学报(自然科学版), 2007, 20(4): 395-398.
WANG Shi-fei, WANG Juan, WANG Hai-xia. Anaysis of an SIRS Epidemic Model with an Age-dependent Vaccination[J]. Journal of Xinyang Normal University (Natural Science Edition), 2007, 20(4): 395-398.
Citation: WANG Shi-fei, WANG Juan, WANG Hai-xia. Anaysis of an SIRS Epidemic Model with an Age-dependent Vaccination[J]. Journal of Xinyang Normal University (Natural Science Edition), 2007, 20(4): 395-398.

具有接种疫苗年龄结构的SIRS流行病模型分析

Anaysis of an SIRS Epidemic Model with an Age-dependent Vaccination

  • 摘要: 建立和研究了具有接种疫苗年龄结构的SIRS流行病模型.运用微分方程和积分方程理论,得到一个与接种疫苗有关的再生数的表达式.证明了当R(0)1时,无病平衡态是全局吸引的.当R(ψ)1时,无病平衡态是局部渐近稳定的;当R(ψ)1时,无病平衡态是不稳定的,此时存在一个地方病平衡态.最后给出地方病平衡态局部渐近稳定的条件.

     

    Abstract: An SIRS epidemic model with an age-dependent vaccination is considered.By using the theory of differential or integral equation,an explicit formula for the vaccine-dependent reproductive number R(ψ) is first obtained.Next,it is showed that the disease-free steady state is locally asymptotically stable if R(ψ) is less than one and unstable if R(ψ) is larger than one.If R(0)1,then the disease-free equilibrium is global attractor.Moreover,there exists an endemic steady state in this model which is unstable un...

     

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