论文标题
流行病：了解起伏和衰减
Epidemics: towards understanding undulation and decay
论文作者
论文摘要
感染水平的波动（通常称为波浪）尚不清楚。在本文中，我们提出了一个数学模型，该模型表现出朝向稳定状态的波动和衰减。该模型是对原始SIR模型的重新解释，该模型通过假设不同的本构关系获得了与恢复的经典逻辑生长。恢复关系基于以下前提：传染性仅持续一段时间。这导致了一个差异差异（延迟）方程，该方程本质上在其溶液中表现出周期性，但不一定会衰减渐近稳定的平衡。确实可以发生极限周期。管理方程式的适当线性化为启发式推理以及对数值计算的信心提供了坚定的基础。
Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original SIR-model obtained by postulating different constitutive relations whereby classical logistic growth with recovery is obtained. The recovery relation is based on the premise that infectiousness only lasts for some time. This leads to a differential-difference (delay) equation which intrinsically exhibits periodicity in its solutions but not necessarily decay to asymptotically stable equilibrium. Limit cycles can indeed occur. An appropriate linearization of the governing equation provides a firm basis for heuristic reasoning as well as confidence in numerical calculations.
