非线性传染率的随机SIS传染病模型的持久性和灭绝性

J4 ›› 2013, Vol. 48 ›› Issue (10): 68-77.

非线性传染率的随机SIS传染病模型的持久性和灭绝性

周艳丽1,2,张卫国1

1. 上海理工大学理学院, 上海 200093; 2. 上海医疗器械高等专科学校, 上海 200093

收稿日期:2013-01-17 发布日期:2013-10-14
作者简介:周艳丽(1976- ),女,讲师,博士研究生,研究方向为生物数学.Email:zhouyanli-math@163.com
基金资助:
国家自然科学基金资助项目(11071164);上海医疗器械高等专科学校校科研启动基金资助项目(A25001201-8)

Persistence and extinction in stochastic SIS epidemic model with nonlinear incidence rate

ZHOU Yan-li1,2, ZHANG Wei-guo1

1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. Shanghai Medical Instrumentation College, Shanghai 200093, China

Received:2013-01-17 Published:2013-10-14

摘要/Abstract

摘要：

讨论了一类具有非线性传染率的随机 SIS 传染病模型。证明了该模型全局惟一正解的存在性; 研究了模型解的长期渐近行为: 当R0≤1时, 证明了模型的无病平衡点是随机全局渐近稳定的; 当R0>1时, 证明了随机系统的解围绕确定性模型的地方病平衡点震荡, 进而得到了疾病平均持续存在以及疾病随机灭绝的充分条件。数值仿真验证了文中主要结论的正确性。

关键词: 随机SIS模型;Lyapunov函数;灭绝性;布朗运动; 伊藤公式

Abstract:

A stochastic SIS epidemic model with nonlinear incidence is investigated. First, the existence of global positive solution is obtained; Next, the asymptotic behaviors of the model are studied that is if R0≤1, the disease-free equilibrium is stochastically asymptotical stability, and if R0>1 the solution is oscillating around the endemic equilibrium of the deterministic model. Furthermore, the sufficient conditions of persistence in the mean and stochastic extinction are obtained. Finally, the theoretical results are illustrated by numerical simulations.

Key words: stochastic SIS epidemic model; Lyapunov function; extinction; Brownian motion； It formula

中图分类号:

O175.1

周艳丽1,2,张卫国1. 非线性传染率的随机SIS传染病模型的持久性和灭绝性[J]. J4, 2013, 48(10): 68-77.

ZHOU Yan-li1,2, ZHANG Wei-guo1. Persistence and extinction in stochastic SIS epidemic model with nonlinear incidence rate[J]. J4, 2013, 48(10): 68-77.

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