Shigui Ruan
Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
Abstract
Measles, a highly contagious infection caused by the measles virus, is a major public-health problem in China. The reported measles cases decreased dramatically from 2004 to 2012 due to the mandatory measles vaccine program started in 2005 and the goal of eliminating measles by 2012. However, after reaching its lowest level in 2012, measles has resurged again since 2013. Since the monthly data of measles cases exhibit a seasonally fluctuating pattern, based on the measles model in Earn et al. (Science 287(2000), 667-670) we propose a susceptible, exposed, infectious, and recovered (SEIR) model with periodic transmission rate to investigate the seasonal measles epidemics and the effect of vaccination. We calculate the basic reproduction number R_0, analyze the dynamical behavior of the model, and use the model to simulate the monthly data of measles cases reported in China. We also carry out some sensitivity analysis of R_0 in the terms of various model parameters which shows that measles can be controlled and eventually eradicated by increasing the immunization rate, improving the effective vaccine management, and enhancing the awareness of people about measles. Age-structured measles models are also considered and optimal vaccination programs are discussed.