Mathematical model for the transmission of mumps and its optimal control

Mumps is a viral contagious disease associated with puffy cheeks and tender and swollen jaw. It spreads through direct contact with saliva or respiratory droplets from the mouth, nose or throat of infected persons. In this work, we present a mathematical model which describes the dynamics of the disease in a human population. The model incorporates isolation and treatment of infected individuals as a control measure. It is shown that the disease-free equilibrium (DFE) is locally and globally asymptotically stable when the control reproduction number R_c is less than one. It is also shown that the model has a unique endemic equilibrium which exists when R_c > 1. The existence of a unique endemic equilibrium confirms the global stability of the DFE, and the absence of backward bifurcation in the model. Optimal control analysis is performed on the model to obtain the proportion of infected humans to be isolated for optimal control of the disease. Plots are presented to show the dynamics of the disease in the presence of the control measures.