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author:

Jiang, H. (Jiang, H..) [1] | Chen, L. (Chen, L..) [2] | Wei, F. (Wei, F..) [3] | Zhu, Q. (Zhu, Q..) [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. © 2023 the Author(s)

Keyword:

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

Community:

  • [ 1 ] [Jiang H.]School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350116, China
  • [ 2 ] [Jiang H.]Fujian Key Laboratory of Financial Information Processing, Putian University, Putian, 351100, China
  • [ 3 ] [Chen L.]School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350116, China
  • [ 4 ] [Wei F.]School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350116, China
  • [ 5 ] [Wei F.]Center for Applied Mathematics of Fujian Province, Fuzhou University, Fuzhou, 350116, China
  • [ 6 ] [Zhu Q.]School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, 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 HC Threshold:13

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count: 1

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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