Global stability of a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy

Abstract

We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment. The treatment rate has at most a finite number of jump discontinuities in every compact interval. By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis, the basic reproductive number [Formula: see text] is proved to be a sharp threshold value which completely determines the dynamics of the model. If [Formula: see text], then there exists a disease-free equilibrium which is globally stable. If [Formula: see text], the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable. We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment. Furthermore, the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.