Global stability of the steady states of an SIS epidemic reaction-diffusion model
Global stability of the steady states of an SIS epidemic reaction-diffusion model
复制标题
SIS 流行病反应扩散模型稳态的全局稳定性
DOI：
10.1016/j.na.2008.10.043
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发表时间：
2009-07-01
影响因子：
1.4
通讯作者：
Liu, Shengqiang
中科院分区：
文献类型：
--
作者：
Peng, Rui;Liu, Shengqiang
本文研究了艾伦等人在[L.J.S.艾伦，B.M. Bolker，Y. Lou，A.L. Nevai，SIS流行病反应扩散模型稳态的渐近分布，离散连续。Dyn. A 21（1）（2008）1-20]。在这两种情况下：（11）易感个体的扩散速率d（S）等于感染个体的扩散速率d（I）;（2）对于任意固定常数r ∈（0，无穷大），beta（x）= r gamma（x），其中beta（x）和gamma（x）分别表示疾病传播和疾病恢复的速率。我们完全确定了无病平衡点和唯一地方病平衡点（如果存在）的全局稳定性。我们的结果部分回答了艾伦等人提出的猜想。（C）2008爱思唯尔有限公司版权所有。
In this work, we investigate the SIS epidemic reaction-diffusion model under heterogeneous environment studied by Allen et al. in [L.J.S. Allen, B.M. Bolker, Y. Lou, A.L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. A 21 (1) (2008) 1-20]. In the two cases: (11) the diffusion rate d(S) of the susceptible individuals is equal to the diffusion rate d(I) of the infected individuals; (2) beta(x) = r gamma(x) for any fixed constant r epsilon (0, infinity), where beta(x) and gamma(x) respectively represent the rates of disease transmission and disease recovery. we completely determine the global stability of the disease-free equilibrium and the unique endemic equilibrium (if it exists). Our results partially answer the conjecture proposed by Allen, et al. (C) 2008 Elsevier Ltd. Ail rights reserved.