Stochastic reversal of deterministic selection in epidemic strain competition

TL;DR

This paper reveals that stochastic effects can reverse deterministic strain advantages in epidemic models, significantly shorten fixation times, and are interpretable through an effective potential framework.

Contribution

It demonstrates that stochastic fluctuations can overturn deterministic predictions and drastically reduce fixation times in a two-strain epidemic model.

Findings

Stochastic effects can reverse deterministic strain advantage.

Fixation times are reduced from years to days due to noise.

A universal scaling law relates fixation time to noise and proximity to quasi-neutrality.

Abstract

Different strains competing for a common pool of susceptible individuals is a key problem in mathematical epidemiology. To address this problem, we investigate a two-strain model within a Susceptible-Infected-Recovered (SIR) framework. While classical deterministic theory predicts that the basic reproduction number fully determines selection, we show that stochastic effects play a key role in the dynamics. We discover that stochastic fluctuations can reverse the deterministic advantage even far from the quasi-neutral regime. Further, we find that stochasticity drastically reduces fixation times from years, in the deterministic case, to days. The fixation time is non-linearly proportional to the noise intensity and the distance from the quasi-neutral regime, following a universal rule obtained from a scaling law. The nature of the problem and the equations allow us to interpret the competition as a dynamical evolution around an effective potential, with the potential barrier corresponding to the unstable manifold associated with the coexistence. Even in a stable situation of dominance of one strain, the noise can induce crossings through the potential. We find that the reversal can occur even far from the quasi-neutral regime with significant probability.