Revisiting the standard for modeling the spread of infectious diseases

The COVID-19 epidemic brought to the forefront the value of mathematical modelling for infectious diseases as a guide to help manage a formidable challenge for human health. A standard dynamic model widely used for a spreading epidemic separates a population into compartments—each comprising individuals at a similar stage before, during, or after infection—and keeps track of the population fraction in each compartment over time, by balancing compartment loading, discharge, and accumulation rates. The standard model provides valuable insight into when an epidemic spreads or what fraction of a population will have been infected by the epidemic’s end. A subtle issue, however, with that model, is that it may misrepresent the peak of the infectious fraction of a population, the time to reach that peak, or the rate at which an epidemic spreads. This may compromise the model’s usability for tasks such as “Flattening the Curve” or other interventions for epidemic management. Here we develop an extension of the standard model’s structure, which retains the simplicity and insights of the standard model while avoiding the misrepresentation issues mentioned above. The proposed model relies on replacing a module of the standard model by a module resulting from Padé approximation in the Laplace domain. The Padé-approximation module would also be suitable for incorporation in the wide array of standard model variants used in epidemiology. This warrants a re-examination of the subject and could potentially impact model-based management of epidemics, development of software tools for practicing epidemiologists, and related educational resources.