An age–gender-structured mathematical model to study the optimization of COVID-19 vaccination programs

We construct an age-structured mathematical model that considers comorbidity status, vaccine hesitancy and gender in order to analyze the efficacy of a very large variety of COVID-19 vaccination programs. We investigate these programs during the early vaccination phase of the COVID-19 pandemic and use the specific time-varying vaccine availability of the USA to approximate the situation in the real world. The epidemiological model is based on a large non-autonomous system of nonlinear differential equations that is solved numerically. The number of fatalities and the years of life lost (YLL) are used to evaluate the optimality of each of the vaccination programs. Due to the numerous factors that influence the infected cases and fatalities, determining the optimal vaccination program is a very complex problem from different points of view. The novel mathematical model includes the effect of social contacts between different demographic groups and the behavior of vaccine hesitant people. We developed, adapted, and implemented three different new optimization algorithms to find the best vaccination programs that minimize the selected metric. These programs differ in the prioritization of the vaccination of each demographic group of the model. The optimization processes found that the best strategies prioritize middle aged male and female individuals without comorbidities. A second vaccination target prioritizes middle aged male individuals with comorbidities. These results are based on the particular behavior of people with comorbidities and taking into account that the case fatality rate of males is higher than for females. The findings of this study highlight the importance of developing an optimal vaccination program with the intention of saving lives and supporting rational vaccine recommendations for other potential pandemics.