Laboratory for Industrial and Applied Mathematics (LIAM), Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada.
Math Biosci Eng. 2020 Nov 4;17(6):7671-7691. doi: 10.3934/mbe.2020390.
We propose a stage-structured model of childhood infectious disease transmission dynamics, with the population demographics dynamics governed by a certain family and population planning strategy giving rise to nonlinear feedback delayed effects on the reproduction ageing and rate. We first describe the long-term aging-profile of the population by describing the pattern and stability of equilibrium of the demographic model. We also investigate the disease transmission dynamics, using the epidemic model when the population reaches the positive equilibrium (limiting equation). We establish conditions for the existence, uniqueness and global stability of the disease endemic equilibrium. We then prove the global stability of the endemic equilibrium for the original epidemic model with varying population demographics. The global stability of the endemic equilibrium allows us to examine the effects of reproduction ageing and rate, under different family planning strategies, on the childhood infectious disease transmission dynamics. We also examine demographic distribution, diseases reproductive number, infant disease rate and age distribution of disease, and as such, the work can be potentially used to inform targeted age group for optimal vaccine booster programs.
我们提出了一个具有年龄结构的儿童传染病传播动力学模型，其中人口统计动态由特定的家庭和人口规划策略控制，对繁殖、衰老和速率产生非线性反馈延迟效应。我们首先通过描述人口统计模型的平衡模式和稳定性来描述人口的长期老龄化状况。我们还使用人口达到正平衡点时的传染病模型（极限方程）来研究疾病传播动态。我们建立了疾病地方病平衡点存在、唯一性和全局稳定性的条件。然后，我们证明了具有变化人口统计数据的原始传染病模型的地方病平衡点的全局稳定性。地方病平衡点的全局稳定性使我们能够在不同的计划生育策略下，研究繁殖衰老和速率对儿童传染病传播动态的影响。我们还检查了人口统计分布、疾病繁殖数、婴儿疾病率和疾病的年龄分布，因此，这项工作可以用来为最佳疫苗加强计划确定目标年龄组。
