Backward,Hopf bifurcation in a heroin epidemic model with treat age  

作　　者：Soufiane Bentout Salih Djilali Behzad Ghanbari 

机构地区：[1]Laboratoire d’Analyse Non Lin´eaire et Math´ematiques Appliqu´ees Universit´e de Tlemcen,Tlemcen,Algeria [2]Department of Basic Science Kermanshah University of Technology,Kermanshah,Iran [3]Faculty of Exact and Computer Sciences Mathematic Department,Hassiba Benbouali University,Chlef,Algeria [4]§Department of Mathematics and Informatics Belhadj Bouchaib University Center of Ain Temouchent,BP 284 RP 46000,Algeria

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2021年第2期198-222,共25页建模、仿真和科学计算国际期刊（英文）

基　　金：S.Bentout and S.Djilali are partially supported by the DGRSTD of Algeria No.C00L03UN130120200004.

摘　　要：Heroin is considered as damage on the health of the individuals.In this paper,we consider a heroin epidemic model with treat age,where the inner rivalry in between the drug users for a small dose of drugs is investigated.The influence of treatment period for a drug consumer before quitting treatment is investigated,where it is obtained that the considered model can undergo backward bifurcation,which shows the possibility of having two endemic equilibriums,this type of bifurcation is discussed in terms of the basic reproduction number R0.The bifurcation diagram is drown in the case of an age structured model.Also,we show the existence of Hopf bifurcation is shown under suitable conditions on the model parameters.The obtained mathematical results are confirmed numerically.

关 键 词：Backward bifurcation heroin epidemic age-structured model HOPFBIFURCATION 

分 类 号：O17[理学—数学]