具有密度制约的非自治SIRS传染病模型的持久性与灭绝性（英文）

许明星; 滕志东; 张龙

doi:10.13568/j.cnki.651094.2015.01.007

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具有密度制约的非自治SIRS传染病模型的持久性与灭绝性（英文）

数理科学 | 更新时间：2026-01-21

- 具有密度制约的非自治SIRS传染病模型的持久性与灭绝性（英文）
- 具有密度制约的非自治SIRS传染病模型的持久性与灭绝性（英文）
- 新疆大学学报（自然科学版中英文） 2015年32卷第1期页码：33-39
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  Supported by the National Natural Science Foundation of P.R.China(11271312,11001235);the China Postdoctoral Science Foundation(20110491750);the Natural Science Foundation of Xinjiang(2012211B07,2011211B08)
- DOI：10.13568/j.cnki.651094.2015.01.007
  中图分类号： O175
- 纸质出版：2015
- 稿件说明：
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[1]许明星,滕志东,张龙.具有密度制约的非自治SIRS传染病模型的持久性与灭绝性（英文）[J].新疆大学学报(自然科学版),2015,32(01):33-39.
[1]许明星,滕志东,张龙.具有密度制约的非自治SIRS传染病模型的持久性与灭绝性（英文）[J].新疆大学学报(自然科学版),2015,32(01):33-39. DOI： 10.13568/j.cnki.651094.2015.01.007.

DOI：10.13568/j.cnki.651094.2015.01.007.

摘要

研究了一类具有密度制约的非自治SIRS传染病模型

获得了疾病持久与灭绝的阈值R*0

R*1和R*2.当R*0≤0或R*1<0时

疾病灭绝;当R*2>0时

疾病持久.特别地

讨论了周期与概周期的情形

得到了基本再生数R0.当R0≤1时

疾病灭绝;当R0>1时

疾病持久.

Abstract

A nonautonomous SIRS epidemic model with density dependence is proposed and studied. Threshold values R*0

R*1and R*2for the permanence and extinction of the disease are established. It is shown that the disease is extinct if R**0≤ 0 or R1< 0 and the disease is permanent if R*2> 0. As applications

the periodic and almost periodic models are discussed. The basic reproductive numbers R0 are obtained. It is shown that the disease is extinct if R0≤ 1 and the disease is permanent if R0> 1.

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references

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