Global threshold dynamics of an age structured alcoholism model

被引：9
作者：
Bentout, Soufiane [1 ,2 ]
Djilali, Salih [1 ,3 ]
Chekroun, Abdenasser [1 ,4 ]
机构：
[1] Univ Tlemcen, Lab Anal Non Lineaire & Math Appl, Tilimsen 13000, Algeria
[2] Belhadj Bouchaib Univ, Dept Math & Informat, Ctr Ain Temouchent, Ain Temouchent 46000, Algeria
[3] Hassiba Benbouali Univ, Fac Exact & Comp Sci, Math Dept, Chlef, Algeria
[4] Univ Abou Bekr Belkaid Tlemcen, Tilimsen 13000, Algeria
来源：
INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2021年 / 14卷 / 03期
关键词：
Mathematical biology; age-structured partial differential equations; alcohol model; uniform persistence; global behavior; Lyapunov function; PREDATOR-PREY MODEL; EPIDEMIC MODEL; HERD SHAPE; SPATIOTEMPORAL PATTERNS; MATHEMATICAL-ANALYSIS; STABILITY; BIFURCATION; DIFFUSION; BEHAVIOR; IMPACT;
D O I：
10.1142/S1793524521500133
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We consider in this research an age-structured alcoholism model. The global behavior of the model is investigated. It is proved that the system has a threshold dynamics in terms of the basic reproduction number (BRN), where we obtained that alcohol-free equilibrium (AFE) is globally asymptotically stable (GAS) in the case R-0 <= 1, but for R-0 > 1 we found that the system persists and the nontrivial equilibrium (EE) is GAS. Furthermore, the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated, which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations. The obtained mathematical results are tested numerically next to its biological relevance.
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页数：34
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