We develop an automatic control system to help to design efficient
mitigation measures for the Covid-19 epidemic in cities. Taking into
account parameters associated to the population of each city and the
mobility among them, the optimal control framework suggests the level
and duration of protective measures that must be implemented to
ensure that the number of infected individuals is within a range that
avoids the collapse of the health care system. Compared against other
mitigation measures that are implemented simultaneously and in equal
strength across cities our method has three major particularities when:
Accounts for city commute and health infrastructure: It takes
into account the daily commute among cities to estimate the dynamics of
infected people while keeping the number of infected people within a
desired level at each city avoiding the collapse of its health care system.
City-specific control: It allows for orchestrating the
control measures among cities so as to prevent all cities to face the
same level control. The model tends to induce alternation between periods
of stricter controls and periods of a more normal life in each city and
among the cities.
Flexible scenarios: It is flexible enough to
allow for simulating the impact of particular actions. For example, one can
simulate the how the control all cities change when the number of care beds
increases in specific places.
Therefore, our method creates an automatic dance adjusting mitigation levels
within cities and alternating among cities as suggested in~\cite{Pue2020}. This
automatic dance may help the city economy and orchestration of resources.
We provide case studies using the major cities of the state of Sao Paulo
given by using estimates on the daily mobility among the cities their health care
system capacity. We use official data in our case studies. However,
sub-notification of infected people in Brazil is notoriously high. Hence the
case study should not be considered as a real world policy suggestion. It high
sub-notification is taken into account, the optimal control algorithm will suggest
stricter mitigation measures, as also shown in the case studies. Surprisingly,
the total duration of the protocol for the state is barely affected by the
sub-notification, but the severity of such protocols is strengthened.
This stresses a twofold implication, first, the protocol depends on high-quality
data and, second, such optimal and orchestrated protocol is robust and can be
adjusted to the demand.