A simple criterion to design optimal non-pharmaceutical interventions for mitigating epidemic outbreaks

Abstract

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and societal costs. Here, we derive a simple and mathematically rigorous criterion for designing optimal transitory non-pharmaceutical interventions for mitigating epidemic outbreaks. We find that reducing the reproduction number below one is sufficient but not necessary. Instead, our criterion prescribes the required reduction in the reproduction number according to the desired maximum of disease prevalence and the maximum decrease of disease transmission that the interventions can achieve. We study the implications of our theoretical results for designing non-pharmaceutical interventions in 16 cities and regions during the COVID-19 pandemic. In particular, we estimate the minimal reduction of each region’s contact rate necessary to control the epidemic optimally. Our results contribute to establishing a rigorous methodology to design optimal non-pharmaceutical intervention policies for mitigating epidemic outbreaks.

Toward more realistic social distancing policies via advanced feedback control

“…• How should one modify the above approach and simulations when vaccinations and variants are taken into account? See, e.g., [Arruda et al(2021)], [Kopfovál et al(2021)], [Laguzet & Turinici(2015)], [Moore et al(2021)], [d'Onofrio et al(2007)], [Ramos et al(2021)] for some preliminary modeling issues.…”

“…The social distancing strategies and in particular the severe lockdown measures due to the worldwide COVID-19 pandemic (see, e.g., [Adolph et al(2021)]) have stimulated a huge number of mathematically oriented investigations among which we select control-theoretic publications: See, e.g., [Al-Radhawi et al(2022)], [Ames et al(2020)], [Angulo et al(2021)], [Berger(2022)], [Bisiacco & Pillonetto(2021)], [Bisiacco et al(2022)], [Bliman & Duprez(2021)], [Bliman et al(2021)], [Bonnans & Gianatti(2020)], [Borri et al(2021)], [Charpentier et al(2020)], [Dias et al(2022)], [Di Lauro et al(2021a)],…”

“…g ., [Adolph et al(2021)]) have stimulated a huge number of mathematically oriented investigations among which we select control-theoretic publications: See, e . g ., [Al-Radhawi et al(2022)], [Ames et al(2020)], [Angulo et al(2021)], [Berger(2022)], [Bisiacco & Pillonetto(2021)], [Bisiacco et al(2022)], [Bliman & Duprez(2021)], [Bliman et al(2021)], [Bonnans & Gianatti(2020)], [Borri et al(2021)], [Charpentier et al(2020)], [Dias et al(2022)], [Di Lauro et al(2021a)], [Di Lauro et al(2021b)], [Efimov & Ushirobira(2021)], [Esterhuizen et al(2021)], [Fliess et al(2022)], [Gevertz et al(2021)], [Greene & Sontag(2021)], [Ianni & Rossi(2021)], [Jing et al(2021)], [Köhler et al(2021)], [McQuade et al(2021)], [Morato et al(2020a)], [Morato et al(2020b)], [Morgan et al(2021)], [Morris et al(2021)], [O’Sullivan et al(2020)], [Péni et al(2020)], [Pillonetto et al(2021)], [Sadeghi et al(2021)], [Sontag(2021)], [Stella et al(2022)], [Tsay et al(2020)]. Most diverse viewpoints have been developed.…”

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

“…Of course, the assumption (A1) is restrictive, however, we understand that the control strategy using social isolation is effective only in the early stages of the epidemic (Al-Radhawi et al 2021;Angulo et al 2021;Sontag 2021). After this period, new control variables and pharmacological actions such as vaccination (Zhong et al 2021) must be added to the model so that it makes sense.…”

Decentralized governance may lead to higher infection levels and sub-optimal releases of quarantines amid the COVID-19 pandemic

“…While mobility restriction measures have been taken during several disease outbreaks in history [ 5 – 11 ], the quarantines needed for the COVID-19 pandemic were at global scales that encompass entire countries. Such quarantines have economic and social costs [ 12 , 13 ], and major questions are how restrictive the quarantines should be, and what would be the right timing to release some of the mobility restrictions [ 1 , 2 , 4 , 14 , 15 ]. In practice, however, these decisions are made independently by multiple countries [ 16 – 18 ], or independently by multiple states in countries like the U.S., or even independently by multiple municipal authorities [ 19 ].…”