Mathematical Modeling and Analysis of Alcoholism Epidemics: A Case Study in Ethiopia
محورهای موضوعی : فصلنامه ریاضیTesfaye Sama 1 , Masreshaw Temere 2
1 - Department of Mathematics, College of Natural and Computational Sciences, Haramaya
University, Haramaya, Ethiopia
2 - Department of Mathematics, College of Natural and Computational Sciences, Haramaya
University, Haramaya, Ethiopia
کلید واژه: Alcoholism Epidemics, Compartmental Model, Reproductive Number, Stability Analysis, Lyapunov Function, Numerical Simulation,
چکیده مقاله :
In this paper, we developed deterministic mathematical model of alcoholism epidemics. First, the existence and uniqueness of the formulated model will be studied to show the well-possedness of the model. Second, the major qualitative analysis like alcoholic free equilibrium point (E0), endemic equilibrium point (E∗), basic reproduction number (R0), were computed. From the stability analysis, we found that an alcoholic free equilibrium point is locally asymptotically stable if R0 < 1. The global asymptotic stability of alcoholic free equilibrium point is established using LaSalle’s invariance principle of Lyapunov functions. The sensitivity of model parameters is done using normalized forward sensitivity index. At the end, numerical simulations on the study were conducted using the ODE 45 to confirm our analytic results. It is pointed out that, minimizing the contact rate between the non-drinkers and heavy drinkers, maximizing the number of drinkers that go into treatment can be useful in combating the alcoholism epidemic.
In this paper, we developed deterministic mathematical model of alcoholism epidemics. First, the existence and uniqueness of the formulated model will be studied to show the well-possedness of the model. Second, the major qualitative analysis like alcoholic free equilibrium point (E0), endemic equilibrium point (E∗), basic reproduction number (R0), were computed. From the stability analysis, we found that an alcoholic free equilibrium point is locally asymptotically stable if R0 < 1. The global asymptotic stability of alcoholic free equilibrium point is established using LaSalle’s invariance principle of Lyapunov functions. The sensitivity of model parameters is done using normalized forward sensitivity index. At the end, numerical simulations on the study were conducted using the ODE 45 to confirm our analytic results. It is pointed out that, minimizing the contact rate between the non-drinkers and heavy drinkers, maximizing the number of drinkers that go into treatment can be useful in combating the alcoholism epidemic.
