具有饱和接触率的SIQRS预防接种模型的控制策略

吉林大学学报(理学版)

具有饱和接触率的SIQRS预防接种模型的控制策略

赵明¹, 吕显瑞²

1. 北华大学数学与统计学院, 吉林吉林 132013； 2. 吉林大学数学学院, 长春 130012

收稿日期:2015-06-29 出版日期:2016-03-26 发布日期:2016-03-23
通讯作者: 吕显瑞 E-mail:lvxr@jlu.edu.cn

Control Strategies of SIQRS Vaccinate Model with Saturating Contact Rate

ZHAO Ming¹, LV Xianrui^2

1. School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2015-06-29 Online:2016-03-26 Published:2016-03-23
Contact: LV Xianrui E-mail:lvxr@jlu.edu.cn

摘要/Abstract

摘要：

建立并分析一类具有饱和接触率、隔离项和脉冲预防接种的SIQRS传染病模型. 通过综合运用Floquet定理、脉冲微分不等式和极限系统理论, 获得了保证SIQRS传染病模型的无病周期解全局渐近稳定的阈值条件. 通过比较脉冲预防接种和隔离两种控制策略的有效性, 表明同时使用脉冲预防接种和隔离两种策略比单独应用一种策略更有效.

关键词: SIQRS传染病模型, 脉冲预防接种, 隔离, 无病周期解, 基本再生数

Abstract:

A SIQRS epidemic model with saturating contact rate, isolation term and impulsive vaccination was established and analyzed. By means of Floquet theorem, impulsive differential inequality and limit system theory, the global asymptotic stable threshold conditions of diseasefree periodic solution in the SIQRS epidemic model were obtained. Comparing the effectiveness of the two control strategies of impulsive vaccination and isolation shows that using the two strategies concurrently is superior to only one strategy for eradicating the disease.

Key words: SIQRS epidemic model, impulsive vaccination, isolation, diseasefree periodic solution, basic reproduction number

中图分类号:

O175.13

赵明, 吕显瑞. 具有饱和接触率的SIQRS预防接种模型的控制策略[J]. 吉林大学学报(理学版), 2016, 54(02): 171-176.

ZHAO Ming, LV Xianrui. Control Strategies of SIQRS Vaccinate Model with Saturating Contact Rate[J]. Journal of Jilin University Science Edition, 2016, 54(02): 171-176.