The global scientific community has been successful in their efforts to develop, test, and commercialize vaccines for COVID-19. However, the limited supply of these vaccines remains to be a widespread problem as different nations have started their respective vaccine rollouts. Policymakers continue to deal with the difficult task of determining how to allocate them. This research work will present how the use of mathematical models can provide valuable decision support under such conditions. Both a linear programming model and a nonlinear programming model have been developed to determine the optimal allocation of COVID-19 vaccines that minimize fatalities and COVID-19 transmission, respectively. These scenarios have to be dealt with when not enough vaccines are available, and the pandemic is still in progress. The model is capable of handling large scale allocation problems such as those intended for the general population of a country. It could also be scaled down for organizations such as private companies or universities. The model also considers multiple vaccines with different levels of efficacy. The distribution of vaccines reduces transmission and relative infectiousness of individuals across different age groups. A hypothetical case study is solved to illustrate the computational capability of the models. The results indicate that priority should be given to the elderly when fatalities are minimized. In contrast, the younger population should then be prioritized when the objective shifts to suppressing contagion.