Optimising the assignment of swabs and reagent for PCR testing during a viral epidemic

Early large-scale swab testing is a fundamental tool for health authorities to assess the prevalence of a virus and enact appropriate mitigation measures during an epidemic. The COVID-19 pandemic has shown that the availability of chemical reagent required to carry out the tests is often a bottleneck in increasing a country's testing capacity. Further, demand is unevenly spread between more affected regions (which require more tests they can perform) and less affected ones (which have spare capacity). These issues hint at the opportunity of increasing test capacity via the optimal allocation of swabs and reagent to laboratories. We prove that this is the case, proposing an Integer Programming formulation to maximise the number of tests a country can perform and validating our approach on both real-life data from Italy and synthetic instances. Our results show that increased inter-regional collaboration and a steadier supply of reagent (i.e., coming from local production sites rather than international shipments) can dramatically increase testing capacity. Accordingly, we propose short-term and long-term recommendations for policy makers and health authorities.