Optimal vaccination strategies using a distributed model applied to COVID-19

Optimal distribution of vaccines to achieve high population immunity levels is a desirable aim in infectious disease epidemiology. A distributed optimal control epidemiological model that accounts for vaccination was developed and applied to the case of the COVID-19 pandemic. The model proposed here is nonstandard and takes into account the heterogeneity of the infected sub-population with respect to the time since infection, which is essential in the case of COVID-19. Based on the epidemiological characteristics of COVID-19 we analyze several vaccination scenarios and an optimal vaccination policy. In particular we consider random vaccination over the whole population and the prioritization of age groups such as the elderly and compare the effects with the optimal solution. Numerical results of the model show that random vaccination is efficient in reducing the overall number of infected individuals. Prioritization of the elderly leads to lower mortality though. The optimal strategy in terms of total deaths is early prioritization of those groups having the highest contact rates.