Threshold dynamics of a multi-group SEAR alcoholism model with public health education

In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number R0 plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium P0 of the model is globally asymptotically stable if R0≤1,while the alcohol-present equilibrium P* exists uniquely and is globally asymptotically stable if R0>1.For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.