Optimal Allocation of Vaccines in a Meta-Population to Control COVID-19 in Sri Lanka

Studying the spread of communicable diseases in a meta-population rather than a single population can provide more insight into the behavior of the spread of the diseases. Human mobility influences the disease-spreading patches and is applied to the model via a mobility matrix M. The optimal control theory is employed to control the disease burden while minimizing the cost of infected individuals and the cost of implementing a control strategy. This research proposes to model a SIR-type model for meta-population to control and reduce disease outbreaks such as COVID-19 by optimizing vaccine allocation in Sri Lanka. By using Kmeans clustering, provinces are further divided into regions according to risk levels. In the absence of control measures, it takes to control the disease burden nearly 3 to 4 years. However, the implementation of control measures, such as vaccination, significantly controls the disease burden. Taking into account that the available control measure capacity reaches its maximum of 0.8, high-risk regions require around two months to control the disease; moderate and low-risk regions require nearly a month to control the disease. The basic reproduction number Ro represents a significant result and it predicts the average number of new cases in the entire population. In contrast, the effective reproduction number (Rt) represents the risk level of the disease when taking into account the current susceptible population. A final epidemic size (ci) represents the cumulative sum of infected individuals in each patch, which plays an important role in representing the patch-specific cost value of infected individuals. Policymakers are able to make decisions such as controlling the spread of disease and maintaining the public and private health sectors as well as the economy of the country based on the results.