Optimal Control of an SIR Model with Delay in State and Control Variables

Elhia, Mohamed; Rachik, Mostafa; Benlahmar, Elhabib

doi:10.1155/2013/403549

Cited by 27 publications

(22 citation statements)

References 9 publications

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“…We use compartmental epidemiological models to describe the spreading of the infection [1], [2], and we view these models as control systems where human intervention is the control input. Viewing epidemiological models as control systems has been proposed in the literature recently [3]- [5], and various models with varying transmission rate [6]- [9] have appeared to quantify the level of human interventions in the case of COVID-19. Illustration of the SIR model as control system and its fit to US COVID-19 data [10].…”

Section: Introductionmentioning

confidence: 99%

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

Molnár

Singletary

Orosz

et al. 2021

IEEE Control Syst. Lett.

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We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. Furthermore, we discuss how measurement delays originated from incubation period and testing delays affect safety and how delays can be compensated via predictor feedback. We demonstrate our results by synthesizing active intervention policies that bound the number of infections, hospitalizations and deaths for epidemiological models capturing the spread of COVID-19 in the USA.

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Section: Introductionmentioning

confidence: 99%

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

Molnár

Singletary

Orosz

et al. 2021

IEEE Control Syst. Lett.

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“…It is important to note that for the SIR model, and the corresponding optimization problem in Eq. (31), N is fixed at a value below the total population. This is necessary due to the underreporting of infections 43 , along with the fact that many people will never have any contact with infected individuals.…”

Section: Methodsmentioning

confidence: 99%

“…We, therefore, will formalize this perspective by making the control aspect of epidemiological models explicit. Note that viewing compartmental epidemiological models as control systems is not unique 31,32 , but has found only limited application to COVID-19 33 and has yet to enjoy formal guarantees on safety. Additionally, there are examples of control-theoretic concepts being applied, namely in the the context of time-varying 27,34 and state-varying 6,35 choices of the transmission rate; these can be viewed as time- and state-varying inputs to a control system.…”

Section: Introductionmentioning

confidence: 99%

Safety-Critical Control of Active Interventions for COVID-19 Mitigation

Ames

Molnár

Singletary

et al. 2020

Preprint

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The world has recently undergone the most ambitious mitigation effort in a century, consisting of wide-spread quarantines aimed at preventing the spread of COVID-19. The use of influential epidemiological models of COVID-19 helped to encourage decision makers to take drastic non-pharmaceutical interventions. Yet, inherent in these models are often assumptions that the active interventions are static, e.g., that social distancing is enforced until infections are minimized, which can lead to inaccurate predictions that are ever evolving as new data is assimilated. We present a methodology to dynamically guide the active intervention by shifting the focus from viewing epidemiological models as systems that evolve in autonomous fashion to control systems with an "input" that can be varied in time in order to change the evolution of the system. We show that a safety-critical control approach to COVID-19 mitigation gives active intervention policies that formally guarantee the safe evolution of compartmental epidemiological models. This perspective is applied to current US data on cases while taking into account reduction of mobility, and we find that it accurately describes the current trends when time delays associated with incubation and testing are incorporated. Optimal active intervention policies are synthesized to determine future mitigations necessary to bound infections, hospitalizations, and death, both at national and state levels. We therefore provide means in which to model and modulate active interventions with a view toward the phased reopenings that are currently beginning across the US and the world in a decentralized fashion. This framework can be converted into public policies, accounting for the fractured landscape of COVID-19 mitigation in a safety-critical fashion.

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“…Here, N=S+I+R is independent of time t and denotes the total population size [8] , [18] , [55] , [56] , [69] . The population of India in 2020 is estimated as 1,380,004,385 people at mid-year according to the UN data [57] .…”

Section: Estimation Of Parameters Of Sir Model Of India Using An Actumentioning

confidence: 99%

“…Elhia et al. [8] optimized the SIR epidemic model with time variation and controlled measures of H1N1 data in Morocco. They considered five parameters, namely recruitment rate of susceptible, effective contact rate, natural mortality rate, recovery rate, and disease-induced death rate, for modeling.…”

Section: Introductionmentioning

confidence: 99%

Estimating the parameters of susceptible-infected-recovered model of COVID-19 cases in India during lockdown periods

Bagal¹,

Rath

Barua

et al. 2020

Chaos, Solitons & Fractals

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Highlights From the pandemic scenario of COVID-19 disease cases in all over the world, the outbreak prediction becomes very complex for the emerging scientifically research. Several epidemiological mathematical models of spread are increasing day by day to forecast correctly. Here, the classical SIR modelling approach is carried out to study the different parameters of this model in case of India county. This type of approach analyzed by considering different governmental lock down measures in India. The outcome results showed the extreme interventions should be taken to tackle this type of pandemic situation in near future.

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Optimal Control of an SIR Model with Delay in State and Control Variables

Cited by 27 publications

References 9 publications

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

Safety-Critical Control of Active Interventions for COVID-19 Mitigation

Estimating the parameters of susceptible-infected-recovered model of COVID-19 cases in India during lockdown periods

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