一类SEIQR模型的稳定性分析以及模型仿真  

Simulation and dynamical behavior analysis of the SEIQR epidemic model

作　　者：胡瑞 黄立冬[1] 谭学文[1] 李荣庭 徐权峰 HU Rui;HUANG Li-dong;TAN Xue-wen;LI Rong-ting;XU Quan-feng(School of Mathematics and Computer Science,Yunnan Minzu University,Kunming 650500,China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500

出　　处：《云南民族大学学报（自然科学版）》2022年第6期701-709,共9页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：云南民族大学研究生科研项目(SJXY2020-102).

摘　　要：考虑一类潜伏期和染病期均具有传染性的SEIQR模型,且模型带有常规预防和医学隔离措施,利用再生矩阵方法计算模型的基本再生数R 0.运用Routh-Hurwitz判据,Lyapunov函数以及LaSalle不变集原理证明,当R 0<1时,模型存在唯一的无病平衡点P 0且P 0全局渐近稳定;当R 0>1时,模型存在2个平衡点,无病平衡点P 0不稳定,地方病平衡点P*全局渐近稳定.通过对模型基本再生数的敏感性分析,得出各个参数对传染病传播的影响,并考虑模型中常规预防和医学隔离措施,对模型进行数值模拟,解释和说明措施的必要性和有效性.In this paper,we consider a susceptible-exposed-infectious-quarantined-recovered(SEIQR)model with the routine preventive and medical isolation measures that is infectious during both incubation and infection periods.The basic reproduction number of the model is calculated based on the next-generation matrix method.Then,the Routh-Hurwitz criterion,Lyapunov functions and LaSalle s invariance principle are used to prove that when R 0<1,the model has a unique disease-free equilibrium point(DFE)P 0,which is globally asymptotically stable,while when R 0>1,there are two equilibrium points in the model,namely,the unstable disease-free equilibrium point P 0 and the globally asymptotically stable endemic equilibrium point(DEE)P*.Through the sensitivity analysis of the basic reproduction number of the model,the influence of each parameter on the spread of infectious diseases was obtained.Meanwhile,we also studied the influence of the parameters of the routine preventive and medical isolation measures on the spread of infectious diseases.Finally,the necessity and effectiveness of the measures are explained and illustrated though numerical simulation of the model.

关 键 词：SEIQR模型 基本再生数 敏感性分析 防疫措施 

分 类 号：O175[理学—数学]