A simple stochastic theory of extinction shows rapid elimination of a Sars-like pandemic

Abstract The SARS-Cov-2 pandemic demonstrated the challenge of controlling a zoonotic disease with high infection fatality rates, including the evolution of more transmissible variants. In dealing with future similar pandemics, the question of elimination vs . mitigation is still an open question. Although a complex question, a key neglected component to appraise the elimination strategy is a simple theory predicting the timescales of elimination. Using simple random walk and branching process theory we provide insights on the process of elimination using non-pharmaceutical interventions. We find the distribution of times is an extreme-valued Gumbel distribution with a new stochastic threshold of infections, below which random changes in infection dominate. We also determine that there are two regimes for the effective reproductive number R e —a weak and strong immunity regime— delineated by a new critical value , describing the role of population immunity in the decline of infections. Overall, for the original SARS-Cov-2 variant our results predict rapid extinction —of order months— of an epidemic or pandemic if the reproductive number is kept to ; in a counterfactual scenario with global adoption of an elimination strategy in June 2020, SARS-Cov-2 could have been eliminated world-wide by early January 2021.