A discrete-time analogue preserving the global stability of a continuous SEIS epidemic model

Abstract

In this paper, we show dynamical consistency between the continuous SEIS epidemic model and its discrete-time analogue, that is, both global dynamics of a continuous SEIS epidemic model ‘without delays’ and the positive solutions of the corresponding backward Euler discretization with mesh width are fully determined by the same single-threshold parameter which is the basic reproduction number of the continuous SEIS model. To prove this, we first obtain lower positive bounds for the permanence of this discrete-time analogue for and then apply a discrete version of Lyapunov function technique in the paper [12].