We define the basic reproductive number for the models.The basic reproductive number is the average of secondary infections produced by a typical infective during the entire period of infectiousness .

• 在研究中对这些模型引入了再生数，其意义为一个病人在染病期内平均感染的人数，再生数决定平衡解的稳定性及地方病平衡点的存在性。