COVID-19 vaccine incentive scheduling using an optimally controlled reinforcement learning model

Abstract

We model Covid-19 vaccine uptake as a reinforcement learning dynamic between two populations: the vaccine adopters, and the vaccine hesitant. Using data available from the Center for Disease Control (CDC), we calculate a payoff matrix governing the dynamic interaction between these two groups and show they are playing a Hawk-Dove evolutionary game with an internal evolutionarily stable Nash equilibrium (the asymptotic percentage of vaccinated in the population). We then ask whether vaccine adoption can be improved by implementing dynamic incentive schedules that reward/punish the vaccine hesitant, and if so, what schedules are optimal and how effective are they likely to be? When is the optimal time to start an incentive program, and how large should the incentives be? By using a tailored replicator dynamic reinforcement learning model together with optimal control theory, we show that well designed and timed incentive programs can improve vaccine uptake by shifting the Nash equilibrium upward in large populations, but only so much, and incentive sizes above a certain threshold show diminishing returns.