(344e) Ziegler and Nichols Meet Kermack and Mckendrick: Parsimony in Dynamic Models for Epidemiology

The COVID-19 epidemic is widely touted as the first in history for which management strategies relied extensively on modeling. A comprehensive model for the spread of an epidemic was developed in a modeling tour de force by Kermack and McKendrick about a century ago. A simplified version of that model has become widely popular recently, even though it has limitations that its originators had clearly articulated and warned against. In summary, a basic limitation of that simplified version is that it assumes most infected individuals recover in 0 time, thus leading to underprediction of the peak of infectious individuals in an epidemic by a factor of 2. (The subject of "Flattening the Curve" widely publicized in managing COVID-19 aimed, among other targets, at lowering that peak.) One could avoid this limitation by considering model that have higher complexity, with obvious pluses and minuses. The focus of this presentation is to present two novel forms of the simplified Kermack-McKendrick model that predict infectious peaks more accurately yet retain simplicity: The first relies on a Pade' approximation of a corresponding transfer function and the second relies on approximating a probability distribution using the Ziegler-Nichols ideas of approximating a high-order system by one of first order plus time delay. In the spirit of Box's famous dictum, both models are "wrong but useful" and create a simple tool for simple use and communication among experts and non-experts alike.