Global Stability of a Mumps Transmission Model with Quarantine Measure

In this paper, a model of mumps transmission with quarantine measure is proposed and then the control reproduction number [Formula: see text] of the model is obtained. This model admits a unique endemic equilibrium P* if and only if R(c) > 1, while the disease-free equilibrium P(0) always exists. By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem, we first show that the equilibrium P(0) is globally asymptotically stable (GAS) if R(c) ≤ 1; second, we prove that the equilibrium P* is GAS if R(c) > 1. Our results reveal that mumps can be eliminated from the community for [Formula: see text] and it will be persistent for [Formula: see text] , and quarantine measure can also effectively control the mumps transmission.