[1]赵晓静,张 龙*,张德婷.一类具有常数输入和马氏转换的SIQRS模型[J].四川师范大学学报(自然科学版),2019,(05):619-625.[doi:10.3969/j.issn.1001-8395.2019.05.008]
 ZHAO Xiaojing,ZHANG Long,ZHANG Deting.An SIQRS Epidemic Model with Constant Input and Markovian Switching[J].Journal of SichuanNormal University,2019,(05):619-625.[doi:10.3969/j.issn.1001-8395.2019.05.008]
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一类具有常数输入和马氏转换的SIQRS模型()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
619-625
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
An SIQRS Epidemic Model with Constant Input and Markovian Switching
文章编号:
1001-8395(2019)05-0619-07
作者:
赵晓静 张 龙* 张德婷
新疆大学 数学与系统科学学院, 新疆 乌鲁木齐 830046
Author(s):
ZHAO Xiaojing ZHANG Long ZHANG Deting
College of Mathematics and System Science, Xinjiang University, Urumqi 830046, Xinjiang
关键词:
最后通过数值模拟验证结果的准确性.SIQRS传染病模型 马氏转换 持久 灭绝
Keywords:
SIQRS epidemic model Markovian switching permanence extinction
分类号:
O175
DOI:
10.3969/j.issn.1001-8395.2019.05.008
文献标志码:
A
摘要:
研究一类具有常数输入,疾病发生率是标准型,而且带有马氏转换的SIQRS模型.分析系统的全局正性及有界性,得到判断疾病消除与持久的阈值:当R0<1时,系统的任意正解将指数收敛于无病状态; 当R0>1时,疾病将蔓延持续下去成为地区“地方病”.
Abstract:
In this paper, we consider a class of SIQRS epidemic models with constant input and Markovian switching.Analysing its global positivity and boundedness.We establish the threshold value R0: the disease is eradicated almost surely if R0< 1, while the disease persists almost surely if R0> 1.Finally, the results are verified by numerical simulation.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-03-29 接受日期:2018-10-25
基金项目:国家自然科学基金(11861065、11361059、11771373和11702237)和新疆维吾尔自治区重点实验室项目(2016D03022)
*通信作者简介:张 龙(1977—),男,教授,主要从事常微分方程及生物数学研究,E-mail:longzhang_xj@sohu.com
更新日期/Last Update: 2019-07-15