Mathematical Analysis for an Age-Structured Heroin Epidemic Model
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In this paper, an age-structured heroin epidemic model, where the susceptibility of individuals and the relapse of heroin users in treatment are described by two age-dependent variables, is formulated and analyzed. The basic reproduction ratio of the model is derived and proved to be a threshold condition, which completely determines the global behaviors of the model. The asymptotic smoothness of the semiflow generated by the family of solutions, uniform persistence and existence of an interior global attractor have been presented for establishing and defining a Lyapunov functional on this attractor. Some control strategies of heroin and two special cases of the model formulation are addressed.
KeywordsLyapunov functional Global stability Age-structure Heroin model
Mathematics Subject Classification34D23 34K20 92D30
L. Liu is supported by the National Natural Science Foundation of China (11601239). X. Liu is supported by the National Natural Science Foundation of China (11671327). We are grateful to the editors and the anonymous referees for their careful reading and helpful comments which led to great improvement of our manuscript.
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