ANALYSIS OF A MULTI-GROUP ALCOHOLISM MODEL WITH PUBLIC HEALTH EDUCATION UNDER REGIME SWITCHING

Zhenfeng Shi; Daqing Jiang; Ningzhong Shi; Tasawar Hayat; Ahmed Alsaedi

doi:10.11948/20200370

2021 Volume 11 Issue 5

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Zhenfeng Shi, Daqing Jiang, Ningzhong Shi, Tasawar Hayat, Ahmed Alsaedi. ANALYSIS OF A MULTI-GROUP ALCOHOLISM MODEL WITH PUBLIC HEALTH EDUCATION UNDER REGIME SWITCHING[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2279-2302. doi: 10.11948/20200370

Citation:

Zhenfeng Shi, Daqing Jiang, Ningzhong Shi, Tasawar Hayat, Ahmed Alsaedi. ANALYSIS OF A MULTI-GROUP ALCOHOLISM MODEL WITH PUBLIC HEALTH EDUCATION UNDER REGIME SWITCHING[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2279-2302. doi: 10.11948/20200370

ANALYSIS OF A MULTI-GROUP ALCOHOLISM MODEL WITH PUBLIC HEALTH EDUCATION UNDER REGIME SWITCHING

1.
School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, Jilin Province, China
2.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah 121589, Saudi Arabia
3.
College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, China
4.
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

Corresponding author: Email: daqingjiang2010@hotmail.com(D. Jiang)

Abstract

Abstract

In this paper, we study a multi-group stochastic alcoholism model with public health education, which is formulated as a piecewise deterministic Markov process. Through a rigorous analysis, we firstly show that the solution of the stochastic model is positive and global. Then we obtain sufficient conditions for the extinction of alcohol problems. In addition, sufficient conditions for the persistence in the mean of alcoholism are derived. Specifically, in the case of persistence, we prove the existence of positive recurrence of the solution to the model by employing suitable stochastic Lyapunov functions.
- Multi-group model /
- alcoholism /
- markovian switching /
- extinction /
- persistence in the mean /
- positive recurrence
MSC: 34F05, 37Hxx, 60Jxx, 92Bxx

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