Transmission dynamics and optimal control of measles epidemics

Based on the mechanism and characteristics of measles transmission, we propose a susceptible-exposed-infectious-recovered (SEIR) measles epidemic model with vaccination and investigate the effect of vaccination in controlling the spread of measles. We obtain two critical threshold values, lc1 and lc2, of the vaccine coverage ratio. Measles will be extinct when the vaccination ratio l > lc1, endemic when lc2 < l < lc1, and outbreak periodically when l < lc2. In addition, we apply the optimal control theory to obtain an optimal vaccination strategy l ðtÞ and give some numerical simulations for those theoretical findings. Finally, we use our model to simulate the data of measles cases in the U.S. from 1951 to 1962 and design a control strategy. 2015 Elsevier Inc. All rights reserved.