A Simple Model of Epidemics with Pathogen Mutation

TL;DR

This paper models how pathogen mutation and immune memory influence epidemic dynamics, revealing that rapid mutation is necessary for pathogen survival in highly connected populations.

Contribution

It introduces a simple model linking pathogen mutation with immune response, analyzing different epidemic behaviors and the conditions for pathogen persistence.

Findings

Pathogens must mutate rapidly in highly connected populations.

Four distinct epidemic behaviors are identified based on parameters.

Transitions between epidemic states are systematically analyzed.

Abstract

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals, (2) endemic infection (3) periodic epidemic outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.