A two-strain model of infectious disease spread with asymmetric temporary immunity periods and partial cross-immunity

TL;DR

This paper develops a two-strain infectious disease model considering asymmetric temporary immunity and partial cross-immunity, analyzing conditions for strain coexistence and exclusion, validated with COVID-19 variant data.

Contribution

It introduces a novel two-strain model with asymmetric immunity parameters and provides a comprehensive bifurcation and stability analysis, including a reduced hybrid system.

Findings

Disparity in immunity periods influences competitive advantage.

Model predicts potential for strain coexistence or exclusion.

COVID-19 variants show different competitive dynamics over time.

Abstract

We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.