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Using a system of time-dynamical equations, we investigate how daily mobility indices, such as the homestay percentage above the pre-COVID normal (   $$H\%$$  H % ; or  H -forcing), and the vaccinated percentage (   $$V_c\%$$  V c % ; or  V -forcing) impact the net reproductive rate ( R 0) 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  R 0 can explain the new trends in 106 countries. The disease transmission can be controlled by forcing down    $$R0(H,V_c) &lt; 1$$  R 0 ( H , V c ) &lt; 1 with an enforcement of continuous    $$H &gt; 40\%$$  H &gt; 40 % in    $$93\%$$  93 % of countries with    $$0\%$$  0 % vaccinated plus recovered,    $$V_p$$  V p . The required critical    $$H\%$$  H % decreases with increasing    $$V_p\%$$  V p % , dropping it down to    $$20\%$$  20 % with    $$25\% V_p$$  25 % V p , and further down to    $$8\%$$  8 % with    $$50\% V_p$$  50 % V p . However, the regulations on    $$H\%$$  H % 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.

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