The inoculation dilemma: Partial vs Full immunization during the early rollout in a pandemic

COVID-19 demonstrated the extent to which a pandemic can affect billions of lives worldwide. Vaccinations are an effective intervention that reduces the burden of the disease on the population. However, the low availability of vaccine doses coupled with an emerging infection wave calls for efficient dose allocation. We study the tradeoffs between prioritization of partial or full immunization while allocating limited doses with the help of an augmented SIR model. We define the term allocation ratio as the ratio of doses allocated for partial immunization as a proportion of the total available doses. Optimal control theory is used to derive the path traversed by the allocation ratio throughout the vaccine administration program. Numerical insights are obtained by introducing the case study of the Indian state of Tamil Nadu. Results indicate a preference towards full immunization when the active infections are low, while a switch to exclusive partial immunization is observed as the infection wave grows. Sensitivity analysis shows that factors like reduced vaccine availability, higher transmission rate, and high first-dose efficacy promote a quicker switch. The results also indicate significant potential savings of around ₹710 billion ($\sim$ $8.46 billion) in mortality losses compared to the more widely followed pro-rata allocation policies. Hence, our study contributes to the growing discussion around the optimal strategy for vaccine administration with a focus on dose prioritization. The results of our research can help policymakers determine the allocation of limited available doses when faced with rising infection numbers during future pandemics.