A two-phase optimization model that considers risk and accessibility for vaccine allocation and health-care units location

Abstract

In December 2019, the novel virus SARS-CoV-2 appeared causing the COVID-19 pandemic. Healthcare systems globally were primary affected by it due to the increase on medical attention and Intensive Care Units (ICUs) demand. Particularly, Mexico belonged among the top 10 coun- tries with the highest number of confirmed cases, and within the top 5 in global deaths. These indicators required federal authorities to mount complex response actions to eradicate it. One of the concerns to deal with hospitals overload is an effective vaccination plan. For this, we propose a two-phase model to prioritize the Mexican entities with higher levels of vulnerability and risk of hospitalization to address the demand allocation problem in an equitable way. The vulnerability index is obtained through data analysis of a Mexican open database, and the model considers a two-dose vaccination program, and a monthly time horizon. The second phase con- sists of a Maximal Covering Location problem that maximizes a set of accessibility indicators to locate the facilities to cover the maximum Mexican population possible. The models are solved in Gurobi Optimizer commercial software and provides the optimal solution within seconds. The results obtained in the allocation model showed that the first vaccine lots are assigned to Ciudad de Me ́xico which is the entity with highest risk of exposure, and, by August 2021 at least 71% of the population is immunized with vaccine. The second model exposes that when enabling 100% of the available facilities, only 57% of the municipalities has access to vaccination. Moreover a sensitivity analysis is employed to evaluate the effect of the radii and the weights in the solution. For future work, we propose the implementation of mobile units to enhance the accessibility. This way providing an effective and equitable solution for Mexico.