The influence of new drinkers' peer groups on a mathematical model of alcoholism epidemics
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Abstract
This study aimed to develop and analyze a mathematical model for the transmission of alcohol addiction to new drinkers by using the standard method. In our model, the human population is divided into five compartments : susceptible drinkers (S), new drinkers (D), heavy drinkers (H), treatment drinkers (T), and recovered drinkers (R). We proposed the mathematical model of alcohol addiction transmission by nonlinear ordinary differential equation system and analyze the mathematical model by the standard method. We obtained an equilibrium point and the basic reproductive number by using the next generation method and spectral radius. Stabilities of the model are determined by the Routh-Hurwitz criteria and the numerical solutions are considered to support the results. In the model we found the alcohol- free equilibrium point E0(1.45, 0, 0, 0, 0) is local asymptotically stable when the parameter values that we used in the numerical simulations are given 1 = 0.01,
2 = 0.5 and
3 = 0.01. We calculated the basic reproduction number with given to be R0 = 0.0878787 < 0. The alcohol-present equilibrium point E1(1.20339, 0.01511, 0.00548, 0.04876, 0.17732) is local asymptotically stable with parameters
1 = 0.5,
2 = 0.01 and
3 = 0.5 , and the basic reproductive number is estimated to be R0 = 1.1068702 > 1. This implied that reducing the rate of interaction with a group of drinkers will reduce the outbreak of alcohol addiction.
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References
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