Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal

Silva, Cristiana J.; Cruz, Carla; Torres, Delfim F. M.; Munuzuri, Alberto P.; Carballosa, Alejandro; Area, Ivan; Nieto, Juan J.; Fonseca-Pinto, Rui; Fonseca, Rui Passadouro da; Santos, Estevao Soares dos; Abreu, Wilson; Mira, Jorge

The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. It is complemented with an analysis of the Portuguese social network, which allows detecting changes in public opinion and provides a feedback to update the model parameters. With this, we apply control theory to maximize the number of people returning to"normal life"and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.