具有非线性恢复率的随机SIQR模型的阈值动力学-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Threshold Dynamics of Stochastic SIQR Epidemic Model with Nonlinear Recovery Rate

作者:: 孙乾乾1; 赵宇2; 谭德君1; 张树文2; （1.厦门工学院数据科学与智能工程学院，福建厦门 361021；2.集美大学理学院，福建厦门 361021）

Author(s):: SUN Qianqian1; ZHAO Yu2; TAN Dejun1; ZHANG Shuwen2; (1.Data Science and Intelligent Engineering School,Xiamen Institute of Technology,Xiamen 361021,China;2.School of Science,Jimei University,Xiamen 361021,China)

Keywords:: SIQR model; nonlinear recovery rate; positive recurrence; threshold

摘要:: 研究具有饱和发生率和非线性恢复率的随机SIQR流行病模型。证明对于任意给定的初始值，随机模型总是存在唯一的全局正解。得到随机模型的基本再生数R0s，证明该基本再生数是决定疾病灭绝与持久的阈值参数：当R0s<1时，疾病将以概率1灭绝；当R0s>1时，Markov过程是正常返的，即疾病是持久的。

Abstract:: In this paper,a stochastic SIQR epidemic model with saturation incidence rate and nonlinear recovery rate was studied.It was firstly proved that there exists a unique global positive solution for any given initial value.Then,the basic reproduction number R0s was obtained,and it was shown that this basic reproduction number is the threshold parameter that determines the extinction and persistence of the disease:when R0s<1,the disease is extinct with probability 1;when R0s>1,the Markov process is positive recurrence which indicates that the disease will prevail.