具有饱和接种率的传染病模型的稳定性

考虑到实践中有一部分人不愿意接种疫苗，引入1个阈值参数，建立了1个具有饱和接种率的传染病模型，以刻画资源有限情况下的接种策略。定义了模型的基本再生数，讨论了无病平衡点和地方病平衡点的存在性以及全局稳定性。结果表明:一方面人群中不愿接种者的比例影响疾病的消除与否以及不能消除时染病者的比例；另一方面可以适当增加存储疫苗的数量，使得当疾病不能被消除时，染病者的数量可以稳定在一个医疗条件允许的预先设定的水平。

The Stability of an Epidemic Model with Saturation Vaccination

A threshold parameter is introduced to represent some individuals will not vaccinate. An epidemic model with saturation vaccination is proposed to describe the vaccination policy with limited resources. The basic reproduc-tion number is defined. The existence and global stability of disease-free equilibrium as well as endemic equilibrium is investigated. The results obtained in this work indicates that the proportion of those willing not vaccinate plays an important role in whether the disease dies out or not and the ratio of infecteds when the disease persists. It also im-plies that the ratio of infecteds could stabilize at a previously specified level by increasing the amount of vaccines if it is impossible to eradicate.