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Basic reproduction ratios for almost periodic compartmental models with time delay
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.jde.2020.03.027
Lizhong Qiang , Bin-Guo Wang , Xiao-Qiang Zhao

Abstract The theory of basic reproduction ratio R 0 is established for a large class of almost periodic and time-delayed compartmental population models. We first present some dynamical properties for linear almost periodic functional differential systems. By using the product space and evolution semigroup approach, we then prove that R 0 − 1 has the same sign as the exponential growth bound of an associated linear system. As an application, we apply the developed theory to an almost periodic SEIR model with an incubation period and obtain a threshold result on its global dynamics in terms of R 0 . Finally, we present some numerical simulations. Numerical simulations indicate that prolonging the length of incubation period is beneficial for the control of the disease. In addition, a simple model shows that the basic reproduction ratio may be underestimated or overestimated if an almost periodic coefficient is approximated by a periodic one.

中文翻译:

具有时间延迟的几乎周期性隔室模型的基本复制率

摘要 为一大类几乎周期性和时滞的区室种群模型建立了基本再生产率R 0 理论。我们首先介绍线性几乎周期性泛函微分系统的一些动力学特性。通过使用乘积空间和演化半群方法,我们然后证明了 R 0 − 1 与相关线性系统的指数增长界具有相同的符号。作为应用,我们将开发的理论应用于具有潜伏期的几乎周期性的 SEIR 模型,并根据 R 0 获得其全局动态的阈值结果。最后,我们给出了一些数值模拟。数值模拟表明,延长潜伏期有利于疾病的控制。此外,
更新日期:2020-08-01
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