The extinction and persistence of a stochastic model of drinking alcohol

Abstract

The dynamical behavior of stochastic model for drinking evolution is researched in this paper. The drinking evolution criteria is comprised of three distinctive compartments namely, susceptible population S (non-consumers), Risk drinkers R and moderate drinkers M. At first, the Lyapunov function is constructed and analyzed followed by the feasibility and positivity of the solution of the proposed model. The sufficient conditions for the extinction and the persistence of the stochastic drinking model are derived through Lyapunov function. Furthermore, the proposed model is tested for an approximate solution using well known RK4 method. The proposed scheme has been simulated deterministically as well as stochastically. The obtained solutions shows strong convergence to the stochastic solution.

Keywords

• Stochastic drinker model
• Extinction
• Persistence
• Basic reproduction number
• Numerical simulation