Controlling Epidemic Diseases Based only on Social Distancing Level

Abstract

On March 11, 2020, the world health organization (WHO) characterized COVID-19 as a pandemic. When the COVID-19 outbreak began to spread, there was no vaccination and no treatment. To epidemic diseases without vaccines or other pharmaceutical intervention, the only way to control them is a sustained physical distancing. In this work, we propose a simple control law to keep the epidemic outbreak controlled. A sustained physical distancing level is adjusted to guarantee the fastest way to finish the outbreak with the number of hospitalized individuals below the desired value. This technique can reduce the economic problems of social distancing and keeps the health care system working. The proposed controller is a closed-loop approach that uses the number of hospitalized individuals as the feedback signal. It also does not need massive swab tests, which simplify the application of the technique. We do stability analyses of the proposed controller to prove the robustness to uncertainties in the parameters and unmodeled dynamics. We present a version of the proposed controller to operate using steps to reopen, which is relevant to help the decision-makers. The proposed controller is so simple that we can use a spreadsheet to calculate the physical distancing level. In the end, we present a set of numerical simulations to highlight the behavior of the number of hospitalized individuals during an epidemic disease when using the proposed control law. We simulate the proposed controller applied to the ideal case, considering uncertainties, unmodeled dynamics, a 10 days latent period, and different values of the desired number of hospitalized individuals. In all cases, the proposed controller ensures the number of hospitalized individuals lower than the upper limit of a predefined range.

Epidemiological Control of COVID-19 Through the Theory of Variable Structure and Sliding Mode Systems

“…Although our manuscript does not address the aforementioned issues, delay compensation and robustness to disturbances (which may lead to resurgence peaks) and timevarying parametric uncertainties are topics well studied in the sliding mode control literature such that, in the future, our contribution can be expanded in these directions as well. On the other hand, recent contributions in these topics by using others control strategies can be found, for instance, in Castaños and Mondié (2021), Pataro et al (2021) and Dias et al (2021). Such references were included in the revised version of the manuscript.…”

“…From control point of view, Pataro et al (2021) investigate how to apply model predictive control (MPC) algorithms to plan appropriate social distancing policies that mitigate the pandemic effects by considering the states of Bahia and Santa Catarina (Brazil). Dias et al (2021) proposes a control law to adjust the physical distancing level to guarantee the fastest way to finish the outbreak with the number of hospitalized individuals below the desired value. Furthermore, the use of nonlinear control techniques, specifically the sliding mode control (SMC), has been widely used in the literature in several applications (Oliveira et al 2016;Roy and Roy 2020;Andrade et al 2014) and also for the control of infectious diseases (Rohith and Devika 2020;Ibeas et al 2013;Xiao et al 2012).…”

Introduction to Group-Structured-Epidemic Model

“…2020 ; Dias et al. 2021a , b , 2020 ). Resuming, we need to consider social aspects to achieve a better representation of an epidemic disease outbreak.…”

“…The recent publications include non-biological aspects in the models. Some of these works (Davies et al 2020;Duan et al 2020;Canabarro et al 2020) consider age structure, others consider multi-regions (Zakary et al 2017a, b), and some consider multiple factors (Hilton and Keeling 2019;Acemoglu et al 2020;Dias et al 2021aDias et al , b, 2020. Resuming, we need to consider social aspects to achieve a better representation of an epidemic disease outbreak.…”

A Multi-Agent-Based Simulation Model for the Spreading of Diseases Through Social Interactions During Pandemics

“…Purposing to avoid the health system overload, Dias et al ( 2022a ) implements a proportional-integral controller on a compartmental model. Pataro et al ( 2022 ) suggest using model predictive control to plan social distancing policies to mitigate the epidemic’s spread.…”