An epidemic model for an evolving pathogen with strain-dependent immunity

TL;DR

This paper introduces a new epidemic model capturing the dynamics of evolving pathogen strains with strain-dependent immunity, bridging existing models and analyzing pathogen re-emergence and extinction times.

Contribution

It presents a parsimonious epidemic model for evolving strains, including a novel quasi-stationary reproduction number and analysis of strain re-emergence.

Findings

Model captures strain evolution and immunity dynamics.

Reproduction number characterizes pathogen re-emergence.

Simulation explores strain distribution over time.

Abstract

Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains, preventing a build up of immunity in the host population. In this paper, a parsimonious epidemic model is defined that attempts to capture the dynamics of evolving strains within a host population. The `evolving strains' epidemic model has many properties that lie in-between the Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models, due to the fact that individuals can only be infected by each strain once, but remain susceptible to reinfection by newly emerged strains. Coupling results are used to identify key properties, such as the time to extinction. A range of reproduction numbers are explored to characterize the model, including a novel quasi-stationary reproduction number that can be used to describe the re-emergence of the pathogen into a population with `average' levels of strain immunity, analogous to the beginning of the winter peak in influenza. Finally the quasi-stationary distribution of the evolving strains model is explored via simulation.