In this paper,we study a drug epidemic model based on epidemiology by dividing thehuman population into four classes at time t:susceptibles(S),drug users(1),drugusers who are treated in isolation and temporarily quit ...In this paper,we study a drug epidemic model based on epidemiology by dividing thehuman population into four classes at time t:susceptibles(S),drug users(1),drugusers who are treated in isolation and temporarily quit drugs(Q_(T))and drug users whoare treated in isolation and permanently quit drugs(Qp).We obtain the basic repro-duction number Ro of the model and perform its sensitivity analysis.We show that if R_(0)<β1A/μ(μ+δ1)<1,then the drug-free equilibrium is globally asymptotically stable,and if R_(0)>1,there exists an drug-abuse equilibrium and it is locally asymptoticallystable.The proposed model may possess forward and backward bifurcations.Moreover,three different control strategies and numerical results are presented.Through differentadjustments to obtain graphical results,we obtain the best strategy to control the drugepidemic.展开更多
基金This research is supported by National Natural Science Foundation of China.The opening project number is 11801398.
文摘In this paper,we study a drug epidemic model based on epidemiology by dividing thehuman population into four classes at time t:susceptibles(S),drug users(1),drugusers who are treated in isolation and temporarily quit drugs(Q_(T))and drug users whoare treated in isolation and permanently quit drugs(Qp).We obtain the basic repro-duction number Ro of the model and perform its sensitivity analysis.We show that if R_(0)<β1A/μ(μ+δ1)<1,then the drug-free equilibrium is globally asymptotically stable,and if R_(0)>1,there exists an drug-abuse equilibrium and it is locally asymptoticallystable.The proposed model may possess forward and backward bifurcations.Moreover,three different control strategies and numerical results are presented.Through differentadjustments to obtain graphical results,we obtain the best strategy to control the drugepidemic.
