A mathematical analysis of a tuberculosis epidemic model with two treatments and exogenous re-infection  

作　　者：Mehdi Lotfi Azizeh Jabbarit Hossein Kheiri 

机构地区：[1]Department of Applied Mathematics Faculty of Mathematical Sciences University of Tabriz,Tabriz,Iran [2]Marand Faculty of Engineering University of Tabriz,Tabriz,Iran

出　　处：《International Journal of Biomathematics》2020年第8期205-231,共27页生物数学学报（英文版）

摘　　要：In this paper,we propose a mathematical model of tuberculosis with two treatments and exogenous re-infection,in which the treatment is effective for number of infectious individuals and it fails for some other infectious individuals who are being treated.We show that the model exhibits the phenomenon of backward bifurcation,where a stable disease-free equilibrium coexists with a stable endemic equilibria when the related basic reproduction number is less than unity.Also,it is shown that under certain conditions the model cannot exhibit backward bifurcation.Furthermore,it is shown in the absence of re-infection,the backward bifurcation phenomenon does not exist,in which the disease-free equilibrium of the model is globally asymptotically stable when the associated reproduction number is less than unity.The global asymptotic stability of the endemic equilibrium,when the associated reproduction number is greater than unity,is established using the geometric approach.Numerical simulations are presented to illustrate our main results.

关 键 词：TUBERCULOSIS backward bifurcation geometric approach basic reproduction number stability analysis 

分 类 号：O17[理学—数学]