Dynamical regulations on mobility and vaccinations for controlling COVID-19 spread

Using a system of time-dynamical equations, we investigate how daily mobility indices, such as the homestay percentage above the pre-COVID normal ([Formula: see text] ; or H-forcing), and the vaccinated percentage ([Formula: see text] ; or V-forcing) impact the net reproductive rate (R0) of COVID-19 in ten island nations as a prototype, and then, extending it to 124 countries worldwide. Our H- and V-forcing model of R0 can explain the new trends in 106 countries. The disease transmission can be controlled by forcing down [Formula: see text] with an enforcement of continuous [Formula: see text] in [Formula: see text] of countries with [Formula: see text] vaccinated plus recovered, [Formula: see text] . The required critical [Formula: see text] decreases with increasing [Formula: see text] , dropping it down to [Formula: see text] with [Formula: see text] , and further down to [Formula: see text] with [Formula: see text] . However, the regulations on [Formula: see text] are context-dependent and country-specific. Our model gives insights into forecasting and controlling the disease’s transmission behaviour when the effectiveness of the vaccines is a concern due to new variants, and/or there are delays in vaccination rollout programs.