Mathematical Model of Drinking Epidemic
Isaac Kwasi Adu *
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China and Department of Mathematics, Valley View University, Techiman Campus, P.O.Box 183 B/A, Ghana.
Mojeeb AL-Rahman EL-Nor Osman
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China and Department of Mathematics and Computer Science, International University of Africa, P.O.Box 2469, Khartoum, Sudan
Cuihong Yang
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
*Author to whom correspondence should be addressed.
Abstract
A non-linear SHTR mathematical model was used to study the dynamics of drinking epidemic. We discussed the existence and stability of the drinking-free and endemic equilibria. The drinking-free equilibrium was locally asymptotically stable if R0 < 1and unstable if R0 > 1. Global stability of drinking-free and endemic equilibria were also considered in the model, using Lassalle’s invariance principle of Lyapunov functions. Numerical simulations were conducted to confirm our analytic results. Our findings was that, reducing the contact rate between the non-drinkers and heavy drinkers, increasing the number of drinkers that go into treatment and educating drinkers to refrain from drinking can be useful in combating the drinking epidemic.
Keywords: Equilibrium points, drinking free equilibrium, endemic equilibrium, reproductive number, global stability, Lyapunov function