The COVID-19 pandemic has brought many countries to their knees, and the urgency to return to normalcy has never been greater. Epidemiological models, such as the SEIR compartmental model, are indispensable tools for, among other things, predicting how pandemic may spread over time and how vaccinations and different public health interventions could affect the outcome. However, deterministic epidemiological models do not reflect the stochastic nature of the actual infected populations for which the true distribution can never be determined precisely. When embedded in an optimization model, the impact of ambiguous risk can influence the desired outcomes of the mitigating strategy. To address these issues, we first propose a robust epidemiological model, which provides prediction intervals that is specified by the Aumann and Serrano (2008) riskiness index. With suitable approximations, the robust epidemiological optimization model that minimizes the riskiness index can be formulated as a mixed integer linear optimization problem. We illustrate how we can apply the robust epidemiological optimization model for strategic vaccine allocation by minimizing the model's riskiness indices for all the constraints on limiting infections across all time periods, and within a given budget for vaccinations. We conduct a simulation study using parameters estimated from open-source datasets on the COVID-19 pandemic. Simulation results illustrate that our robust vaccine allocation model yields solutions that outperform the benchmark models in controlling the spread of infections.