Tuberculosis transmission with multiple saturated exogenous reinfections  

作　　者：Saduri Das Prashant K.Srivastava Pankaj Biswas 

机构地区：[1]National Institute of Technology Silchar,Assam 88010,India [2]Indian Institute of Technology Patna,Bihar 801103,India

出　　处：《International Journal of Biomathematics》2024年第7期79-109,共31页生物数学学报(英文版)

摘　　要：In this paper,a nonlinear mathematical model for tuberculosis transmission,which incorporates multiple saturated exogenous reinfections,is proposed and explored.The existence of disease-free and endemic steady states is investigated.Disease-free equilibrium(DFE)is locally asymptotically stable(LAS)but not globally asymptotically stable(GAS)when the basic reproduction number,R_(0)<1.However,it is GAS only when there is no exogenous reinfection.The local asymptotic stability and global asymptotic stability of the unique endemic equilibrium point(EEP)are established under certain conditions when R_(0)>1.Further,the EEP is GAS when R_(0)>1,provided there is no exogenous reinfection.When Ro is below unity,the presence of multiple endemic equilibria is found which leads to backward bifurcation.It is demonstrated that the system encounters a Hopf-bifurcation when the transmission rate β crosses a critical value,resulting in the formation of limit cycles,i.e.periodic solutions bifurcate around the EEP whenβpasses a critical value.The stability and direction of Hopf-bifurcation are also studied.The results of the analytical work are validated through numerical simulations.A numerical simulation illustrates that EEP losses its stability via Hopf-bifurcation for specific parameters.However,when the bifurcation parameterβis increased further,the EEP regains its stability.In addition,Hopf-bifurcation occurs due to exogenous reinfection rates p and o.Thus,our model shows some important nonlinear dynamical behaviors.

关 键 词：TUBERCULOSIS exogenous reinfection stability backward bifurcation HOPFBIFURCATION limit cycle stability switch 

分 类 号：O17[理学—数学]