JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (1): 12-22.doi: 10.6040/j.issn.1671-9352.0.2019.040

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Stochastic model of heroin drug dissemination with psychological effects

FANG Shu, ZHANG Tai-lei*, LI Zhi-min   

  1. School of Science, Changan University, Xian 710064, Shaanxi, China
  • Published:2020-01-10

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Abstract: In this paper, considering the relapse of heroin addicts, we establish a stochastic model with psychological effects for the transmission of heroin drugs. The existence of global unique positive solutions of the model is proved by using stopping time theory. When the basic reproduction number of the corresponding deterministic model is equal or less than 1, the heroin-free propagation equilibrium point of the stochastic model is globally randomly asymptotically stable. It shows that the solutions of the stochastic model oscillates near the corresponding deterministic model heroin propagation equilibrium point when the basic reproduction number of the deterministic model is greater than 1. Sufficient conditions are obtained for the average persistence of solutions and the extinction of drugs. Finally, the numerical simulation further shows the dynamic behavior of the model.

Key words: stochastic model, oscillating behavior, persistence, extinction

CLC Number: 

  • O175.1
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