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arXiv · 2604.22876

Stochastic reversal of deterministic selection in epidemic strain competition

Enrique C. Gabrick·Ana Luiza de Moraes·Ervin K. Lenzi·Iberê L. Caldas
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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.

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Enrique C. Gabrick, Ana Luiza de Moraes, Ervin K. Lenzi, Iberê L. Caldas. 2026-04-24. Stochastic reversal of deterministic selection in epidemic strain competition. https://arxiv.org/abs/2604.22876

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