关键词: 麻疹模型, 继发性免疫失败, 基本再生数, 全局稳定性

Abstract: We established a class of measles epidemic model based on secondary vaccine failure induced by vaccination. By using the next generation matrix method, we first obtained the basic reproduction number R₀ of the model and gave its biological meaning, and then proved that R₀ was a sharp threshold parameter by constructing an appropriate Laypunov function. When R₀≤1, the disea
se-free equilibrium is globally asymptotically stable; when R₀>1, the diseasefree equilibrium is unstable and the endemic equilibrium is globally asymptotically stable.

Key words: measles model, secondary vaccine failure, basic reproduction number, global stability