Modeling COVID-19 Optimal Testing Strategies in Retirement Homes: An Optimization-based Probabilistic Approach

Retirement Home facilities have been widely affected by the COVID-19 pandemic. The residents in these homes are usually elderly people with a high risk of mortality from being infected. Since they are in contact with each other, once an infection arrives at the facility, it propagates quickly. To prevent the outbreaks, it has been demonstrated that regular testing of the residents is the most practical approach. However, testing may result in extra time for the staff that performs the test as well as residents' discontent, which presents a trade-off between the time invested in testing, daily caring activities, and viral spread containment. We introduce a novel optimization approach for testing schedule strategies in retirement homes. We develop a mixed-integer linear programming model for balancing the staff’s workload while minimizing the expected detection time of a probable infection inside the facility. We present a probabilistic approach in conjunction with the optimization models to compute the risk of infection, including contact rates, incidence status, and the probability of infection of the residents. To tackle the combinatorial nature of the problem, we proved an efficient property, called symmetry property of optimal testing strategy and utilized it in proposing an enhanced local search algorithm. We perform several experiments with real-size instances and show that the proposed approach can derive optimal testing strategies.