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author:

Jiang, Hui (Jiang, Hui.) [1] | Chen, Ling (Chen, Ling.) [2] (Scholars:陈玲) | Wei, Fengying (Wei, Fengying.) [3] (Scholars:魏凤英) | Zhu, Quanxin (Zhu, Quanxin.) [4]

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Abstract:

We study a switching heroin epidemic model in this paper, in which the switching of supply of heroin occurs due to the flowering period and fruiting period of opium poppy plants. Precisely, we give three equations to represent the dynamics of the susceptible, the dynamics of the untreated drug addicts and the dynamics of the drug addicts under treatment, respectively, within a local population, and the coefficients of each equation are functions of Markov chains taking values in a finite state space. The first concern is to prove the existence and uniqueness of a global positive solution to the switching model. Then, the survival dynamics including the extinction and persistence of the untreated drug addicts under some moderate conditions are derived. The corresponding numerical simulations reveal that the densities of sample paths depend on regime switching, and larger intensities of the white noises yield earlier times for extinction of the untreated drug addicts. Especially, when the switching model degenerates to the constant model, we show the existence of the positive equilibrium point under moderate conditions, and we give the expression of the probability density function around the positive equilibrium point.

Keyword:

extinction Fokker-Planck equation heroin model probability density function regime switching stationary distribution

Community:

  • [ 1 ] [Jiang, Hui]Fuzhou Univ, Sch Math & Stat, Fuzhou 350116, Peoples R China
  • [ 2 ] [Chen, Ling]Fuzhou Univ, Sch Math & Stat, Fuzhou 350116, Peoples R China
  • [ 3 ] [Wei, Fengying]Fuzhou Univ, Sch Math & Stat, Fuzhou 350116, Peoples R China
  • [ 4 ] [Jiang, Hui]Putian Univ, Fujian Key Lab Financial Informat Proc, Putian 351100, Peoples R China
  • [ 5 ] [Wei, Fengying]Fuzhou Univ, Ctr Appl Math Fujian Prov, Fuzhou 350116, Peoples R China
  • [ 6 ] [Zhu, Quanxin]Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China

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Source :

MATHEMATICAL BIOSCIENCES AND ENGINEERING

ISSN: 1547-1063

Year: 2023

Issue: 7

Volume: 20

Page: 13222-13249

2 . 6 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:13

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count: 1

SCOPUS Cited Count: 1

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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