Modeling seasonal measles transmission in China

• A discrete-time deterministic measles model with periodic transmission rate is proposed.
• The basic reproduction number is calculated by the method of spectral radius.
• Threshold dynamics of the model in terms of basic reproduction number are investigated by using the persistence theory.
• A case study on the transmission of measles in China is to validate the model well.

A discrete-time deterministic measles model with periodic transmission rate is formulated and studied. The basic reproduction number R0R0 is defined and used as the threshold parameter in determining the dynamics of the model. It is shown that the disease will die out if R0<1R0<1, and the disease will persist in the population if R0>1R0>1. Parameters in the model are estimated on the basis of demographic and epidemiological data. Numerical simulations are presented to describe the seasonal fluctuation of measles infection in China.