Should We Delay the Second COVID-19 Vaccine Dose in Order to Optimize Rollout? A Mathematical Perspective

Soulaimane Berkane, Intissar Harizi, Abdelhamid Tayebi, Michael S Silverman, Saverio Stranges

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


Objectives: With vaccination shortage persisting in many countries, adopting an optimal vaccination program is of crucial importance. Given the slow pace of vaccination campaigns globally, a very relevant and burning public health question is whether it is better to delay the second COVID-19 vaccine shot until all priority group people have received at least one shot. Currently, many countries are looking to administer a third dose (booster shot), which raises the question of how to distribute the available daily doses to maximize the effectively vaccinated population. Methods: We formulate a generalized optimization problem with a total of u T = ∑ i = 1 n u i vaccine doses, that have to be optimally distributed between n different sub-populations, where sub-population u i represents people receiving the ith dose of the vaccine with efficacy α i . The particular case where n = 2 is solved first, followed by the general case of n dose regimen. Results: In the case of a two dose regimen, if the efficacy of the second dose is less than (or equal to) twice the efficacy of the first dose, the optimal strategy to maximize the number of effectively vaccinated people is to delay the second vaccine as much as possible. Otherwise, the optimal strategy would consist of administering the second dose as quickly as possible. In the general case, the optimal vaccination strategy would be to administer the k - th dose corresponding to the index providing the maximum inter-dose efficacy difference (α i - α i-1) for all possible values of i ∈ {1, … , n}, with α 0 = 0. Conclusion: Our results suggest that although extending the interval between doses beyond 12 weeks was likely optimal earlier in the pandemic, the reduced single dose efficacy of vaccines against the delta variant make this approach no longer viable.

Original languageEnglish
Pages (from-to)1604312
JournalInternational Journal of Public Health
Publication statusPublished - 24 Jan 2021


  • COVID-19
  • COVID-19 Vaccines
  • Humans
  • SARS-CoV-2
  • Vaccination


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