Shigui Ruan

Modeling the Seasonal Transmission Dynamics of Measles

Abstract
Measles, a highly contagious infection caused by the measles virus, is a
major public-health problem worldwide. 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. Then we consider an
age-structured version of the periodic measles model. After establishing
the well-posedness of the initial-boundary value problem, we study the
existence of time periodic solutions of the model by using the fixed point
theorem. We also carry out some sensitivity analysis of R_0 in the terms
of model parameters showing 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.
Finally we will briefly discuss optimal vaccination programs in
age-structured measles models.