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一类具扩散的SIRS传染病模型解的渐近性质 被引量：2

Asymptotic Properties of Solutions to a SIRS Epidemic Model With Diffusion
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摘要 研究了一类具有非线性发生率的SIRS传染病模型的弱耦合反应扩散方程组.利用线性化和特征值的方法,讨论了无病平衡点和染病平衡点的局部稳定性,利用Liapunov函数的方法给出了无病平衡点渐近稳定的充分条件.结果表明,在小初值条件下,当接触率小的时候,无病平衡点是渐近稳定的. The weakly coupled reaction-diffusion system describing a SIRS epidemic model with nonlinear incident rate is investigated. The local asymptotic stabilities of equilibriums are given by linearization and eigenvalue. The asymptotic stabilities of disease-free equilibrium is investigated using the method of Liapunov functions. Our results show that the disease-free equilibrium is asymptotically stable if the contact rate is small and the initial values are small.
作者 甘文珍 史一欢
机构地区 江苏技术师范学院数理学院 南京师范大学生命科学学院
出处 《南京师大学报（自然科学版）》 CAS CSCD 北大核心 2009年第3期25-30,共6页 Journal of Nanjing Normal University(Natural Science Edition)
基金 江苏省教育厅自然科学基金(BK2006064)资助项目
关键词 非线性发生率 暂时免疫力 时滞 反应扩散系统 渐近性质 nonlinear incident rate temporary immunity time delay reaction diffusion system asymptotic properties
分类号 O175.26 [理学—基础数学]
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参考文献13

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二级参考文献16

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共引文献15

同被引文献6

引证文献2

二级引证文献1

南京师大学报（自然科学版）
2009年 第3期

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