An iterative algorithm for optimizing COVID-19 vaccination strategies considering unknown supply

Abstract

Background and objective: The distribution of the newly developed vaccines presents a great challenge in the ongoing SARS-CoV-2 pandemic. Policy makers must decide which subgroups should be vaccinated first to minimize the negative consequences of the pandemic. These decisions must be made upfront and under uncertainty regarding the amount of vaccine doses available at a given time. The objective of the present work was to develop an iterative optimization algorithm, which provides a prioritization order of predefined subgroups. The results of this algorithm should be optimal but also robust with respect to potentially limited vaccine supply.

Methods: We present an optimization meta-heuristic which can be used in a classic simulation-optimization setting with a simulation model in a feedback loop. The meta-heuristic can be applied in combination with any epidemiological simulation model capable of depicting the effects of vaccine distribution to the modeled population, accepts a vaccine prioritization plan in a certain notation as input, and generates decision making relevant variables such as COVID-19 caused deaths or hospitalizations as output. We finally demonstrate the mechanics of the algorithm presenting the results of a case study performed with an epidemiological agent-based model.

Results: We show that the developed method generates a highly robust vaccination prioritization plan which is proven to fulfill an elegant supremacy criterion: the plan is equally optimal for any quantity of vaccine doses available. The algorithm was tested on a case study in the Austrian context and it generated a vaccination plan prioritization favoring individuals age 65+, followed by vulnerable groups, to minimize COVID-19 related burden.

Discussion: The results of the case study coincide with the international policy recommendations which strengthen the applicability of the approach. We conclude that the path-dependent optimum optimum provided by the algorithm is well suited for real world applications, in which decision makers need to develop strategies upfront under high levels of uncertainty.

Fig 1. Iterative algorithm to optimize the distribution of the batches.

The algorithm is started with an empty state and is terminated as soon as the sum of all state-exponents matches a predefined maximum iteration number.

Fig 2. Model results for daily COVID-19 caused deaths after every step of the iterative optimization algorithm.

In each step, one additional batch has been distributed. The target variable for the optimization algorithm is the number of cumulative COVID-19 caused deaths.

Fig 3. Model results for daily COVID-19 caused deaths for simulations performed during the second step of the optimization algorithm.

Each line represents one of the enhancements ${\left(x_1^{\prime }\right)}^i,i\in \{Y,M,E,V,H\}$ with x₁ = E. The target variable for the optimization algorithm is the number of cumulative COVID-19 caused deaths.

Fig 4. Accumulated model results for daily COVID-19 caused deaths for all the simulations performed during the iterative optimization.

After each step / batch, the simulation enhances the batch-notation that yielded the best results for the target variable. In the last iteration, EEEE led to an invalid plan since the corresponding group G_E is already fully vaccinated after EEE.