Should We Delay the Second COVID-19 Vaccine Dose?

Harizi, I.; Berkane, S.; Tayebi, A.

Due to the shortage in COVID-19 vaccine supplies and the alarming sanitary situation engendered by the COVID-19 pandemic, some countries have opted to delay the second dose of the COVID-19 vaccine for some period of time, aiming at getting the first dose of the vaccine to a large number of the population, before proceeding with the second doses. This strategy has sparked some heated debates world-wide for its pros and cons, and no clear consensus is reached among experts. Without taking side in this matter, we tried to answer the following question, from a pure mathematical perspective: should we delay the second dose of the vaccine or not?. We show that the answer to this question depends tightly on the efficacy of the first and the second COVID-19 vaccine doses. In particular, if the first dose is more than 50% efficient, the optimal procedure to maximize the number of effectively vaccinated sub-population is to delay the second vaccine as much as possible (the maximum period between the two doses prescribed by the clinical recommendations). On the other hand, if the efficacy of the first dose is less than 50% and the efficacy of the second dose exceeds a certain threshold, then it would be optimal to administer the second dose as quickly as possible (while respecting the minimum period between the two does as prescribed by the clinical recommendations). We provide explicitly the expression of this threshold as a function of the efficacy of first dose.