Stochastic reversal of deterministic selection in epidemic strain competition

Original 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.