Department of Applied Mathematics, Changchun University of Science and Technology, Changchun, Jilin 140022, PR China.
School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116023, PR China.
Math Biosci. 2019 Feb;308:27-37. doi: 10.1016/j.mbs.2018.12.003. Epub 2018 Dec 7.
We investigate an SIR epidemic model with discrete age groups to understand the transmission dynamics of an infectious disease in a host population with an age structure. We derive the basic reproduction number R and show that it is a sharp threshold parameter. If R≤1, the disease-free equilibrium E is globally stable. If R>1,E is unstable, the model is uniformly persistent, and an endemic equilibrium exists. The global stability of the endemic equilibrium when R>1 is established under a sufficient condition. The model is then used to analyze the measles data in India and evaluate the effectiveness of several vaccination strategies for the control of measles epidemics in India.
我们研究了一个具有离散年龄组的 SIR 传染病模型，以了解具有年龄结构的宿主群体中传染病的传播动态。我们推导出基本再生数 R，并表明它是一个尖锐的阈值参数。如果 R≤1，则无病平衡点 E 是全局稳定的。如果 R>1，E 是不稳定的，模型是一致持久的，并且存在地方病平衡点。在充分条件下，建立了 R>1 时地方病平衡点的全局稳定性。然后，该模型用于分析印度的麻疹数据，并评估几种疫苗接种策略在控制印度麻疹流行中的有效性。
