带潜伏期和年龄结构流行病模型的稳定性

Stability of an Age-structured Epidemic Model with Latent Period

根据肺结核的传播特点,建立了带潜伏期和潜伏年龄的数学模型.证明了当基本再生数R0<1时,系统无病平衡点是局部和全局渐近稳定的;当R0>1时,无病平衡点不稳定,此时系统存在一个地方病平衡点,并证明了该地方病平衡点是局部渐近稳定的.

Based on the infection characteristics of TB,an age-structured epidemic model with latent period is studied.It is proved that the disease-free equilibrium is locally and globally asymptotically stable if R0〈1,one endemic equilibrium exists if R0〉1,and the stability conditions of endemic equilibrium are also given.