Optimal control of the COVID-19 pandemic with non-pharmaceutical interventions

Perkins, T. Alex; España, Guido

doi:10.1101/2020.04.22.20076018

Cited by 42 publications

(43 citation statements)

References 47 publications

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“…Analyses since have indicated that such measures were effective across a wide range of geographic settings ( 48 – 51 ). Even so, acting sooner could have prevented even more cases and deaths ( 52 ).…”

Section: Discussionmentioning

confidence: 99%

Estimating unobserved SARS-CoV-2 infections in the United States

Perkins

Cavany

Moore

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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By March 2020, COVID-19 led to thousands of deaths and disrupted economic activity worldwide. As a result of narrow case definitions and limited capacity for testing, the number of unobserved severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections during its initial invasion of the United States remains unknown. We developed an approach for estimating the number of unobserved infections based on data that are commonly available shortly after the emergence of a new infectious disease. The logic of our approach is, in essence, that there are bounds on the amount of exponential growth of new infections that can occur during the first few weeks after imported cases start appearing. Applying that logic to data on imported cases and local deaths in the United States through 12 March, we estimated that 108,689 (95% posterior predictive interval [95% PPI]: 1,023 to 14,182,310) infections occurred in the United States by this date. By comparing the model’s predictions of symptomatic infections with local cases reported over time, we obtained daily estimates of the proportion of symptomatic infections detected by surveillance. This revealed that detection of symptomatic infections decreased throughout February as exponential growth of infections outpaced increases in testing. Between 24 February and 12 March, we estimated an increase in detection of symptomatic infections, which was strongly correlated (median: 0.98; 95% PPI: 0.66 to 0.98) with increases in testing. These results suggest that testing was a major limiting factor in assessing the extent of SARS-CoV-2 transmission during its initial invasion of the United States.

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Section: Discussionmentioning

confidence: 99%

Estimating unobserved SARS-CoV-2 infections in the United States

Perkins

Cavany

Moore

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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“…The model proposed here is an extension of the classical models based on ordinary differential equations that tackled the issue of the optimal control of COVID-19 outbreak [30][31][32][33]. Here, the whole population is structured by age (a) and additionally by the time since infection (i) for infectious individuals, which echoes the model developed in [50] using a discrete-time formulation of the infection.…”

Section: Discussionmentioning

confidence: 99%

“…Here, more specifically, we look for the intevention that significantly reduces morbidity associated with COVID-19 at a minimal cost. In the same context, mathematical modeling using optimal control theory has been carried out to identify optimal strategies involving non-pharmaceutical interventions to control infectious diseases such as influenza and COVID-19 [30][31][32][33]. However, none of these models take into account the age structure of the host population or the variation of the infectiousness with the time since infection.…”

Section: Introductionmentioning

confidence: 99%

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

Richard

Alizon

Choisy

et al. 2020

Preprint

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In an epidemic, individuals can widely differ in the way they spread the infection, for instance depending on their age or on the number of days they have been infected for. The latter allows to take into account the variation of infectiousness as a function of time since infection. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g.} social distancing) are of great importance to mitigate the pandemic. We propose a model with a double continuous structure by host age and time since infection. By applying optimal control theory to our age-structured model, we identify a solution minimizing deaths and costs associated with the implementation of the control strategy itself. This strategy depends on the age heterogeneity between individuals and consists in a relatively high isolation intensity over the older populations during a hundred days, followed by a steady decrease in a way that depends on the cost associated to a such control. The isolation of the younger population is weaker and occurs only if the cost associated with the control is relatively low. We show that the optimal control strategy strongly outperforms other strategies such as uniform constant control over the whole populations or over its younger fraction. These results bring new facts the debate about age-based control interventions and open promising avenues of research, for instance of age-based contact tracing.

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“…These include phenomenological models [16,17], stochastic models [18], both of which are very useful in the early stages of the outbreak, and mechanistic models [19,20,22,23,30] that incorporate our understanding of the transmission pathways. Imran et.al [24] and Perkins et.al [31] have used optimal control techniques to propose efficient control strategies. The aim of such modeling is twofold, one to provide estimates of the severity of the outbreak by calculating quantities like the growth trends of the epidemic, estimates of the final outbreak size and duration of the outbreak and second to provide insights into efficacy of various control measures.…”

Section: Introductionmentioning

confidence: 99%

Can medication mitigate the need for a strict lock down?: A mathematical study of control strategies for COVID-19 infection

Ali

Imran

Khan³

2020

Preprint

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BackgroundCOVID-19 is a pandemic that has swept across the world in 2020. To date the only effective control mechanisms were non-pharmaceutical interventions, however there have been encouraging reports regarding possible medication in the literature, with emergency approval given to some drugs in various countries.MethodsWe formulate a deterministic epidemic model to study the effects of medication on the transmission dynamics of Corona Virus Disease (COVID-19). We are especially interested in how the availability of medication could change the necessary quarantine measures for effective control of the disease. We model the transmission by extending the SEIR model to include asymptomatic, quarantined, isolated and medicated population compartments.ResultsWe calculate the basic reproduction number R0 and show that for R0<1 the disease dies out and for R0>1 the disease is endemic. Using sensitivity analysis we establish that R0 is most sensitive to the rates of quarantine and medication. We also study how the effectiveness and the rate of medication along with the quarantine rate affect R0. We devise optimal quarantine, medication and isolation strategies, noting that availability of medication reduces the duration and severity of the lock-down needed for effective disease control.ConclusionOur study also reinforces the idea that with the availability of medication, while the severity of the lock downs can be eased over time some social distancing protocols need to be observed, at least till a vaccine is found. We also analyze the COVID-19 outbreak data for four different countries, in two of these, India and Pakistan the curve is still rising, and in he other two, Italy and Spain, the epidemic curve is now falling due to effective quarantine measures. We provide estimates of R0 and the proportion of asymptomatic individuals in the population for these countries.

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Optimal control of the COVID-19 pandemic with non-pharmaceutical interventions

Cited by 42 publications

References 47 publications

Estimating unobserved SARS-CoV-2 infections in the United States

Estimating unobserved SARS-CoV-2 infections in the United States

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

Can medication mitigate the need for a strict lock down?: A mathematical study of control strategies for COVID-19 infection

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