Global analysis of a network-based SIR epidemic model with a saturated treatment function  

作　　者：Xiaodan Wei 

机构地区：[1]College of Computer Science,Dalian Minzu University,Dalian 116600,P.R.China

出　　处：《International Journal of Biomathematics》2024年第6期269-291,共23页生物数学学报(英文版)

基　　金：The research was supported in part by the NNSFC(grant 12071058);the Applied Basic Research Program of Department of Science and Technology of Liaoning Province of China(grant 2023JH2/101300095).

摘　　要：In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim is to present a global analysis and to investigate how the parameterαaffects the spreading of diseases.Our main results are as follows:(1)In the case of the threshold value R_(0)<1,there exist two values of α:α_(c) and α_(0),such that the disease-free equilibrium is globally asymptotically stable when α≤α_(0) and multiple endemic equilibria exist when α≥α_(0).This means that the parameterαhas an essential infuence on the spreading of the disease.(2)In the case of the threshold value R_(0)>1,if the model has only one endemic equilibrium,then the unique endemic equilibrium is globally attractive.In this case,it is also proved that if α≤α_(c),then the endemic equilibrium has only one,so is globally attractive,In addition,numerical simulation is performed to illustrate our theoretical results.

关 键 词：SIR epidemic model complex network saturated treatment function global stability global attractivity 

分 类 号：O17[理学—数学]