Ziegler and Nichols meet Kermack and McKendrick: Parsimony in dynamic models for epidemiology

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.