赵旭,周文书.具有接种的确定性和随机SIS流行病模型的全局稳定性[J].数学研究及应用,2021,41(1):62~68
具有接种的确定性和随机SIS流行病模型的全局稳定性
Global Stability of the Deterministic and Stochastic SIS Epidemic Models with Vaccination
投稿时间:2020-05-30  修订日期:2020-09-27
DOI:10.3770/j.issn:2095-2651.2021.01.007
中文关键词:  SIS流行病模型  接种  全局稳定性
英文关键词:SIS epidemic model  vaccination  global stability
基金项目:国家自然科学基金(Grant No.12071058).
作者单位
赵旭 北方民族大学数学与信息科学学院, 宁夏 银川 750021
大连民族大学理学院, 辽宁 大连 116600 
周文书 大连民族大学理学院, 辽宁 大连 116600 
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中文摘要:
      研究具有接种的确定性和随机SIS流行病模型地方病平衡点的全局稳定性.确定性SIS流行病模型是李建全和马知恩于2004年建立的.对此模型,此前的一些研究工作仅给出了确保地方病平衡点全局稳定的充分条件.本文利用李雅普诺夫函数方法证明了:当基本再生数比1大时,地方病平衡点是全局稳定的.本文还研究了相应的随机SIS流行病模型,并通过构造新的李雅普诺夫函数给出了确保地方病平衡点全局稳定的充分条件.
英文摘要:
      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.
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