Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme

Abstract EN

In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations.

Threshold dynamics of the continuous model are performed by constructing Lyapunov functions.

The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model.

In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.