  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. After identification of the population readiness to
follow social restrictions, by analyzing the social media, we incorporate this
effect in a version of the model that allow us to check different scenarios.
This is realized by considering a Monte Carlo discrete version of the previous
model coupled via a complex network. Then, we apply optimal 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.
