Lyapunov functions and global stability for a discretized multigroup SIR epidemic model

In this paper, a discretized multigroup SIR epidemic model is constructed by applying a nonstandard finite difference schemes to a class of continuous time multigroup SIR epidemic models. This discretization scheme has the same dynamics with the original differential system independent of the time step, such as positivity of the solutions and the stability of the equilibria. Discrete-time analogue of Lyapunov functions is introduced to show that the global asymptotic stability is fully determined by the basic reproduction number R-0.