均值回归过程扰动下具双重流行假设的随机SIS流行病模型
A Stochastic SIS Epidemic Model with Double Epidemic Hypothesis under Mean Regression Process
李佳琦 1林玉国1
作者信息
- 1. 北华大学数学与统计学院,吉林 吉林 132013
- 折叠
摘要
考虑一类非线性发病率下双重流行假设的随机SIS流行病模型.首先,通过对传播率进行均值回归过程下的扰动,建立随机模型;其次,从理论上证明了随机模型具有唯一的全局正解;再次,通过构造李雅普诺夫函数,得到两种传染病灭绝的充分条件.最后证明了:当R*1>1、R′2<1时,疾病I1 持久,疾病I2 灭绝;当R′1<1、R*2>1 时,疾病I2 持久,疾病I1 灭绝;当R*1>1、R*2>1 时,疾病I1 和I2 均持久.
Abstract
A class of stochastic SIS epidemic model with dual epidemic hypothesis under nonlinear incidence rate is considered.First,a stochastic model is established by perturbing the transmission rate under the mean regression process;Secondly,it has been theoretically proven that the stochastic model has a unique global positive solution;Next,sufficient conditions for the extinction of two infectious diseases are obtained by constructing Lyapunov functions.Finally,it is further derived that when R*1>1,R′2<1,the diseases I1 will persist and I2 will become exti-nct;When R′1<1,R*2>1,the diseases I2 will persist and I1 will become extinct;When R*1>1,R*2>1,the dise-ases I1 and I2 will persist.
关键词
SIS模型/均值回归过程/李雅普诺夫函数Key words
SIS model/mean regression process/Lyapunov function引用本文复制引用
出版年
2025
国家科技期刊平台
NSTL
万方数据