Global dynamics of a delayed alcoholism model with the effect of health education

Shuang Hong Ma; Hai Feng Huo; Hong Xiang; Shuang Lin Jing; Shuang Hong Ma; Hai Feng Huo; Hong Xiang; Shuang Lin Jing

doi:10.3934/mbe.2021048

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 904-932. doi: 10.3934/mbe.2021048

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Global dynamics of a delayed alcoholism model with the effect of health education

1.
Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
2.
College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China

Received: 06 October 2020 Accepted: 08 December 2020 Published: 04 January 2021

An alcohol consumption model with health education and three time delays is formulated and analyzed. The alcoholism generation number is defined. Two steady states of the model are found. At the same time, the corresponding global dynamics of the model are analyzed respectively in four cases with different time delays. Then, the effects of health education and three time delays in controlling the alcohol problem are discussed. Some numerical simulation results are also given to support our theoretical predictions.
- alcoholism model,
- time delays,
- health education,
- global dynamics,
- numerical simulation
Citation: Shuang Hong Ma, Hai Feng Huo, Hong Xiang, Shuang Lin Jing. Global dynamics of a delayed alcoholism model with the effect of health education[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 904-932. doi: 10.3934/mbe.2021048

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Abstract

An alcohol consumption model with health education and three time delays is formulated and analyzed. The alcoholism generation number is defined. Two steady states of the model are found. At the same time, the corresponding global dynamics of the model are analyzed respectively in four cases with different time delays. Then, the effects of health education and three time delays in controlling the alcohol problem are discussed. Some numerical simulation results are also given to support our theoretical predictions.

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