Managing bed capacity and timing of interventions: a COVID-19 model considering behavior and underreporting

We develop a mathematical model considering behavioral changes and underreporting to describe the first major COVID-19 wave in Metro Manila, Philippines. Key parameters are fitted to the cumulative cases in the capital from March to September 2020. A bi-objective optimization problem is formulated that allows for the easing of restrictions at an earlier time and minimizes the number of additional beds ensuring sufficient capacity in healthcare facilities. The well-posedness of the model and stability of the disease-free equilibria are established. Simulations show that if the behavior was changed one to four weeks earlier before the easing of restrictions, cumulative cases can be reduced by up to 55% and the peak delayed by up to four weeks. If reporting is increased threefold in the first three months of the estimation period, cumulative cases can be reduced by 61% by September 2020. Among the Pareto optimal solutions, the peak of cases is lowest if strict restrictions were eased on May 20, 2020 and with at least 56 additional beds per day.