Enhancing ‘disease x’ responsiveness: a risk-averse distributionally robust optimization approach for resource allocation under infectious disease transmission variability

Testing stands out as a crucial element in the public health response during a pandemic, serving diverse purposes pivotal for controlling the spread of the infectious agent. It enables early case detection, facilitating prompt isolation and treatment, thereby reducing the severity of individual cases and interrupting the transmission chain within communities. Recognizing the pivotal role of testing in managing and mitigating the impact of a pandemic, this paper addresses the distribution of test kits, taking into account the spatiotemporal uncertainty in demand and the ambiguity of the demand's probability distribution over a multi-period horizon. Determining decisions about location, allocation, operational distribution, and shipment is the main goal in order to guarantee equity and fairness in the distribution of resources among different populations. A two-stage distributionally robust optimisation (DRO) model is proposed to address the ambiguity in the probability distribution of demand. An equivalent reformulation is derived for this model over $ \mathrm {L_{1}} $ L1-norm and joint $ \mathrm {L_{1}} $ L1- and $ \mathrm {L_{\infty }} $ L∞-norm ambiguity sets. Additionally, a risk-averse criterion is employed to more accurately account for some of the worst realizations of random future demand scenarios. To demonstrate the proposed DRO model's practicality, a numerical analysis of COVID-19 test kit distribution in the US is carried out.