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Mathematical Analysis for an Age-Structured Heroin Epidemic Model

  • Lili Liu
  • Xianning LiuEmail author
Article
  • 40 Downloads

Abstract

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.

Keywords

Lyapunov functional Global stability Age-structure Heroin model 

Mathematics Subject Classification

34D23 34K20 92D30 

Notes

Acknowledgements

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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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  2. 2.Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis, Complex Systems Research CenterShanxi UniversityTaiyuanChina

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