EXTINCTION AND STATIONARY DISTRIBUTION OF A HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS AND MARKOV SWITCHING

Kouling Li; Jinhai Guo; Yongchang Wei

doi:10.11948/20250174

2026 Volume 16 Issue 3

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Kouling Li, Jinhai Guo, Yongchang Wei. EXTINCTION AND STATIONARY DISTRIBUTION OF A HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS AND MARKOV SWITCHING[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1446-1474. doi: 10.11948/20250174

Citation:

Kouling Li, Jinhai Guo, Yongchang Wei. EXTINCTION AND STATIONARY DISTRIBUTION OF A HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS AND MARKOV SWITCHING[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1446-1474. doi: 10.11948/20250174

EXTINCTION AND STATIONARY DISTRIBUTION OF A HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS AND MARKOV SWITCHING

1.
School of Information and Mathematics, Yangtze University, Jingzhou, China

Author Bio: Email: lkl1546162380@163.com(K. Li); Email: xin3fei@21cn.com(J. Guo)
Corresponding author: Email: wyc897769778@yeah.net(Y. Wei)
Fund Project: The second author supported by National Natural Science Foundation of China (No. 11871118)

Abstract

Abstract

This paper endeavors to construct and embark on a rigorous investigation of a heroin epidemic model, subject to influences from both Lévy jumps and regime-switching. The primary objective is to conduct an in-depth analysis of the dynamical behaviors of this complex system. Firstly, we establish sufficient conditions for both the persistence in the mean and the extinction of the heroin epidemic model. Subsequently, under some certain conditions, we demonstrate the existence of a unique stationary distribution for this system. Finally, some numerical examples and figures are presented to illustrate and validate the theoretical results in an intuitive manner.
- Heroin epidemic model /
- Lévy jumps /
- Markov switching /
- extinction /
- stationary distribution
MSC: 60H10, 34D05

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References

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