The COVID-19 crisis popularized the importance of mathematical modeling for managing epidemics. A celebrated pertinent model was developed by Kermack and McKendrick about a century ago. A simplified version of that model has long been used and became widely popular recently, even though it has limitations that its originators had clearly articulated and warned against. A basic limitation is that it unrealistically assumes zero time to recovery for most infected individuals, thus underpredicting the peak of infectious individuals in an epidemic by a factor of as much as about 2. One could avoid this limitation by returning to the original comprehensive model, at the cost of higher complexity. To remedy that, we blend Ziegler-Nichols modeling ideas, developed for automatic controller tuning, with Kermack-McKendrick ideas to develop novel model structures that predict infectious peaks accurately yet retain simplicity. We illustrate these model structures with computer simulations on real epidemiological data.

COVID-19 危机普及了数学模型对流行病管理的重要性。大约一个世纪前，Kermack 和 McKendrick 开发了一个著名的相关模型。该模型的简化版本早已被使用并在最近广受欢迎，尽管它的创始人已经明确表达并警告过它的局限性。一个基本的限制是，它不切实际地假设大多数感染者的恢复时间为零，因此将流行病中感染者的峰值预测低了大约 2 倍。可以通过返回原始综合模型来避免这种限制，以更高的复杂性为代价。为了解决这个问题，我们融合了为自动控制器调整而开发的 Ziegler-Nichols 建模思想，与 Kermack-McKendrick 的想法一起开发新颖的模型结构，可以准确地预测传染性峰值，同时保持简单性。我们通过对真实流行病学数据的计算机模拟来说明这些模型结构。