DYNAMICS OF STOCHASTIC HEROIN EPIDEMIC MODEL WITH L&#201;VY JUMPS

Guangjie Li; Qigui Yang; Yongchang Wei

doi:10.11948/2018.998

2018 Volume 8 Issue 3

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Guangjie Li, Qigui Yang, Yongchang Wei. DYNAMICS OF STOCHASTIC HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 998-1010. doi: 10.11948/2018.998

Citation:

Guangjie Li, Qigui Yang, Yongchang Wei. DYNAMICS OF STOCHASTIC HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 998-1010. doi: 10.11948/2018.998

DYNAMICS OF STOCHASTIC HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS

Department of Mathematics, South China University of Technology, Guangzhou, 510640, China

Fund Project:

Abstract

Abstract

People have paid the surge of attention to the prevention and the control of the heroin epidemic for the number of drug addicts is increasing dramatically. In the study of the heroin epidemic, modeling is an important tool. So far many heroin epidemic models are often characterized by ordinary differential equations (ODEs) and many results about them have been obtained. But unfortunately, there is little literature of stochastic heroin epidemic model with jumps. Based on this point, this paper establishes a class of heroin epidemic models|stochastic heroin epidemic model with Lévy jumps. Under some given conditions, the existence of the global positive solution of such model is first obtained. We then study the asymptotic behavior of this model by applying the Lyapunov technique.
- Stochastic heroin model /
- global positive solution /
- asymptotic behavior /
- Lévy noise
MSC: 92D25;93D20;93E03

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