A Kermack--McKendrick type epidemic model with double threshold phenomenon (and a possible application to Covid-19)

TL;DR

This paper extends the Kermack-McKendrick epidemic model by incorporating a double threshold phenomenon, explaining variability in epidemic severity across similar regions and potentially applying to Covid-19.

Contribution

It introduces a model with infectivity age and resistance thresholds, revealing a double threshold effect and Allee effect in epidemic dynamics, enhancing understanding of outbreak variability.

Findings

Identification of a double threshold phenomenon in epidemic models

Demonstration of an Allee effect influencing epidemic final size

Application potential to Covid-19 epidemic analysis

Abstract

The suggestion by K.L. Cooke (1967) that infected individuals become infective if they are exposed often enough for a natural disease resistance to be overcome is built into a Kermack-McKendrick type epidemic model with infectivity age. Both the case that the resistance may be the same for all hosts and the case that it is distributed among the host population are considered. In addition to the familiar threshold behavior of the final size of the epidemic with respect to a basic reproductive number, an Allee effect is generated with respect to the final cumulative force of infection exerted by the initial infectives. This offers a deterministic explanation of why geographic areas that appear to be epidemiologically similar have epidemic outbreaks of quite different severity.