Dynamics Analysis Of Heroin Transmission Models

Three main models of heroin transmission are studied in the thesis:the heroin transmission model with psychological effect,the stochastic heroin transmission model and the heroin transmission model with seasonality.The thesis consists of six chapters.The research background and status of the heroin transmission model are introduced,the mathematical theories and methods related to the infectious disease models are also given in the first two chapters.A heroin transmission model with the psychological effect is established in the third chapter.The basic reproduction number of the model is given.Then the global asymptotic stability of the drug-free equilibrium point was proved by the Lyapunov function,the Routh-Hurwitz criterion and LaSalle invariant set principle.A stochastic heroin transmission model with the environmental noise is established in the fourth chapter.By the theory of stochastic differential equations and Lyapunov analysis method,the stochastic asymptotical stability of the drug-free equilibrium point and the sufficient conditions of persistence in the mean is proved.A heroin epidemic model with seasonality is established in the fifth chapter.The threshold value<R0>?which determines the extinction and permanence for the model is found.By using Lyapunov functions and Ito formula,it shows that the drug-free equilibrium point is exponentially stable if<R0>?<0.And if<R0>?>0,there is at least one non-trivial positive periodic solution for this model,and the spread of heroin will persist.The main research results of this thesis on the heroin transmission models are summarized,and the problems to be further explored are proposed in the sixth chapter.