Study on epidemic dynamics model with time delay to eliminate measles in China

Abstract

Measles is an infectious illness and especially harmful to children. Although the national immunization program is implemented, measles remains to be an important public health issue in China. This paper is devoted to modelling the combined effects of the first dose of Measles rubella combination vaccines (MR1) and the second dose of Measles mumps rubella combination vaccines (MMR2) coverage rates on the controlling of measles. To do that, we propose and study a robust time delayed compartment measles epidemic model where MMR2 is followed after an interval time τ by MR1. Via simulation method, we find ℜ0 is a decreasing function on the coverage rates of MR1 η1 and the coverage rates of MMR2 η2, but an increasing function on the interval time τ . We also find ℜ0 > 1 based on the Chinese current situation of η1 = 0.95, η2 = 0.95 and τ = 1.25. In order to completely eliminate measles in China, η1 should be more than 0.9643, or η2 should be more than 0.9586, or τ should be within 8 month. By comparison, it is easier to shorten the interval time τ by revising the Chinese national immunization program.