Abstract
This letter studies if and to which extent COVID-19 epidemics can be controlled by authorities taking decisions on public health measures on the basis of daily reports of swab test results, active cases, and total cases. A suitably simplified process model is derived to support the controllability analysis, highlighting the presence of a very significant time delay; the model is validated with data from several outbreaks. The analysis shows that suppression strategies can be effective if strong enough and enacted early on. It also shows how mitigation strategies can fail because of the combination of delay, unstable dynamics, and uncertainty in the feedback loop; approximate conditions based on the theory of limitation of linear control are given for feedback control to be feasible.
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Author Keywords
- Control applications,
- delay systems,
- emerging control applications,
- healthcare and medical systems,
- modeling
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IEEE Keywords
- Mathematical model,
- Public healthcare,
- Feedback control,
- Viruses (medical),
- Delays,
- Sociology,
- Statistics,
- COVID-19
Introduction
The first outbreak of the COVID-19 [1] virus epidemic took place in China, starting at the end of 2019, and has since then caused a global pandemic with disruptive effects on public health, social life, and the economy. The pandemic will likely spark a large number of studies to understand its behavior and to determine effective control strategies.
A wide range of mathematical models have been proposed to describe the dynamic evolution of epidemics, starting from the seminal paper [2], and including a wide range of possibly quite sophisticated models, see, e.g., [3] for a comprehensive review. The analysis of these models allows us to predict the evolution of the disease over time, its asymptotic behavior (e.g., endemic disease equilibria vs. eradication), and most importantly how it depends on the model parameters.
Epidemiological models are widely used to design vaccination and treatment strategies based on optimal control, see, e.g., [4] and references therein. They can also be used to design feedback vaccination strategies [5], or even feedback strategies combining different actions such as vaccination, treatment, and culling [6]. Some studies take into account the feedback effects of behavioral changes in the evolution of an epidemic, see [7], and reference therein.
Most models employed to study control strategies are formulated in terms of ordinary differential equations, e.g., the classical SIR and SEIR models and their variants. In some cases, time delays are also included in the model, to account for the incubation time, see, e.g., [8], [9].
Detailed models of the COVID-19 outbreak have started to appear in the literature. With reference to the outbreak in Italy, [10] proposes an extension of the classic SIR model with eight state variables, while [11] presents a spatially resolved model with nine state variables for each of the 107 provinces of the country. Both models confirmed the appropriateness of the public measures taken by the Italian authorities to contain the virus outbreak. A highly detailed epidemiological model of the U.K. was used in [12] to predict possible outcomes of the virus outbreak and to suggest the adoption of a suppression policy.
The report [13] attempts to estimate the effects of non-pharmaceutical interventions (NPIs, i.e., public health measures) onto the relative reduction of the reproduction number Rt of COVID-19, by applying Bayesian methods to data from 11 European countries. Given the estimates of the initial reproduction number R0 , a reduction by at least 60–70% or more is necessary to suppress exponential growth. The main result of [13] is that lockdown leads to an average reduction of Rt by 50%, school closure by 20%, other measures around 10%. However, 95% confidence intervals on the reduction factors are huge, e.g., 10% to 80% reduction for lockdown, 0% to 45% reduction for school closure, severely undermining their predictive power. This problem is inherent to the requirement of a large enough data set to be statistically significant, which requires to put countries with very different social habits and very different interpretations of the same measure (e.g., lockdown) in the same data set.
The use of feedback control theory has been advocated early on as a powerful tool to support the management of the COVID-19 outbreak [14]. Unfortunately, most of the existing literature on the control of epidemics involve vaccines or treatments, which are currently not available for COVID-19. Some innovative feedback control strategies have been proposed in preprints at the time of this writing, e.g., [15], which proposes a feedback mitigation strategy based on fast lockdown cycles controlled by a supervisory loop, or [16], advocating a strategy based on massive random testing.
The aim of this letter is to assess the controllability of the COVID-19 outbreak, assuming that the population is sufficiently well mixed and that the decisions of public health measures by the authorities are based on daily reports of positive swab tests, active cases, and total cases. To this aim, a suitably simplified model is presented, which is specifically aimed at capturing the fundamental dynamics of the process that is relevant for feedback control, which turns out to be heavily affected by time delay.
The main result of the analysis is twofold. On one hand, suppression strategies can be effective if enacted early on and with strong enough measures. On the other hand, mitigation strategies turn out to be infeasible if the reproduction number is significantly higher than one, and are in any case limited by the time delays in the feedback loop.
This letter is structured as follows. In Section II, a control-oriented model of the epidemic is introduced and validated against data from the outbreaks in different countries. In Section III, the two above-mentioned strategies are analyzed in terms of feedback control. Section IV draws conclusions from the control-theoretical analysis with some recommendations for decision-makers and future research.
Conclusion
Governments all the world over are faced with very challenging life-or-death decisions regarding the management of the COVID-19 epidemic, involving the balance between public health and economic issues. In order to take such decisions, they rely on expert advice based on the results of epidemiological mathematical models and on daily case reports, based on swab test results.
This letter puts the problem in a control systems perspective as a feedback control problem, using a simple model to capture the control-relevant dynamic response of those reports to the application of NPIs. The model was tuned and validated with data from four different outbreaks.
These are the main results of the analysis:
- The suppression strategy is effective if NPIs are strong enough to obtain Rt<1 , but it requires to understand the role of the multiplicative factor M to correctly decide when it is the right time to enforce them.
- Mitigation strategies are limited by the combination of delay, uncertainty, and unstable dynamics. Designing robust stabilizing controllers around trajectories with Rt>1.1 is likely to be difficult or impossible. Reducing the overall delay by 50% would bring the limit to Rt>1.2 . This information is particularly relevant for the management of the reopening phase after lockdown.
- Measurement and decision delays play a crucial role in determining the feedback control performance and stability; hence, they should be explicitly taken into account in the design of any feedback controller, and minimized as much as possible, e.g., by promoting fast testing policies and technologies.
- The analysis and design of NPIs can benefit from control theory tools, possibly suggesting viable solutions or pointing out shortcomings of proposed strategies, that are not obvious to epidemiologists and physicians.
At the time of this writing, the emerging consensus seems to be that the safest policy to address exponentially growing COVID-19 outbreaks is to apply aggressive enough suppression policies; the results reported in this letter can further motivate why this is actually the case.
These results could also be useful to devise effective and safe strategies to cope with the reopening phase that countries face after successfully suppressing the first outbreak, in particular, if the number of new daily cases becomes too large to allow for testing, tracing and tracking of individual cases.
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FULL Paper PDF file:
Can the COVID-19 Epidemic Be Controlled onthe Basis of Daily Test Reports?Bibliography
author
Year
2020
Title
Can the COVID-19 Epidemic Be Controlled onthe Basis of Daily Test Reports?
Publish in
in IEEE Control Systems Letters, vol. 5, no. 3, pp. 1079-1084, July 2021,
Doi
10.1109/LCSYS.2020.3009912.
PDF reference and original file: Click here
Somayeh Nosrati was born in 1982 in Tehran. She holds a Master's degree in artificial intelligence from Khatam University of Tehran.
Professor Siavosh Kaviani was born in 1961 in Tehran. He had a professorship. He holds a Ph.D. in Software Engineering from the QL University of Software Development Methodology and an honorary Ph.D. from the University of Chelsea.
Nasim Gazerani was born in 1983 in Arak. She holds a Master's degree in Software Engineering from UM University of Malaysia.
