Optimization of testing protocols to screen for COVID-19: a multi-objective model

In this paper we develop a new multi-objective simulated annealing (MOSA) algorithm to generate optimal testing protocols for infectious diseases, using the COVID-19 pandemic as our context. A SEIR (susceptible-exposed-infected-recovered) epidemiological model is embedded as the computational platform for our MOSA algorithm to optimize testing protocols for screening across three joint objectives: minimum cost of test materials, minimum total infections over the testing horizon, and minimum number of false negatives over the horizon. We demonstrate the application of this optimization tool to recommend screening protocols for K-12 school districts in the U.S. State of North Carolina. Our approach is scalable by population coverage and can be employed at the level of individual school districts or regional collections of districts, individual schools or collections of schools across a district, business sites, or nursing homes, among other congregate settings where individuals may be screened prior to gaining entry to the site. The algorithm can be solved two ways, generating either independent optimal protocols across individual testing locations, or a common protocol covering all locations in the collection of testing sites. Our findings can be used to inform policy decisions to guide the development of effective testing strategies for controlling the spread of COVID-19 or other pandemic diseases in a wide range of congregate settings across various geographic regions.