Global stability analysis of two-stage Quarantine-Isolation model with Holling Type II incidence function

Abstract

new two-stage model for assessing the effect of basic control measures, quarantine and isolation, on a general disease transmission dynamic in a population is designed and rigorously analyzed. The model uses the Holling II incidence function for the infection rate. First, the basic reproduction number (R0) is determined. The model has both locally and globally asymptotically stable disease-free equilibrium whenever R0 < 1. If R0 > 1, then the disease is shown to be uniformly persistent. The model has a unique endemic equilibrium when R0 > 1. A nonlinear Lyapunov function is used in conjunction with LaSalle Invariance Principle to show that the endemic equilibrium is globally asymptotically stable for a special case.