具有隔离和不完全治疗的传染病模型的全局稳定性

摘要/Abstract

摘要：

该文建立了一类具有隔离和不完全治疗的传染病模型.在模型中考虑了无意识和有意识的易感人群，通过基本再生数确定了模型的传播动力学，当$R_{0}≤1$时，无病平衡点是全局渐近稳定的，当$R_{0}>1$时，地方病平衡点是全局渐近稳定的，并通过数值模拟说明了理论分析的正确性.

关键词: 传染病模型, 基本再生数, 全局稳定性, Lyapunov泛函

Abstract:

An epidemic model with quarantine and incomplete treatment is constructed. The model allows for the susceptibles to the unconscious and conscious susceptible compartment. We establish that the global dynamics are completely detremined by the basic reproduction number $R_{0}$. If $R_{0}≤1$, then the disease free equilibrium is globally asymptotically stable. If $R_{0}>1$, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to confirm the analytical results.

Key words: Epidemic model, Basic reproduction number, Global stability, Lyapunov functional

中图分类号:

O175.1

丰利香,王德芬. 具有隔离和不完全治疗的传染病模型的全局稳定性[J]. 数学物理学报, 2021, 41(4): 1235-1248.

Lixiang Feng,Defen Wang. Global Stability of an Epidemic Model with Quarantine and Incomplete Treatment[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1235-1248.

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参数	定义
$\Lambda$	出生率
$\beta_{E}$	与潜伏者接触的传播概率
$\beta_{I}$	与感染者接触的传播概率
$\sigma$	有意识的易感者接触率调节因子
$p$	易感者由无意识转为有意识的速率
$r_{1}$	潜伏者转为隔离者的转移率
$r_{2}$	潜伏者转为感染者的转移率
$\varepsilon$	感染者被隔离的速率
$\xi$	接受治疗的速率
$\delta$	治疗失败的速率
$\mu$	自然死亡率
$d$	因病死亡率

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