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Modeling and Control of Epidemics through Testing Policies

Muhammad Umar Niazi 1 Alain Kibangou 1 Carlos Canudas de Wit 1 Denis Nikitin 1 Liudmila Tumash 1 Pierre-Alexandre Bliman 2
1 DANCE - Dynamics and Control of Networks
Inria Grenoble - Rhône-Alpes, GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : Testing is a crucial control mechanism in the beginning phase of an epidemic when the vaccines are not yet available. It enables the public health authority to detect and isolate the infected cases from the population, thereby limiting the disease transmission to susceptible people. However, despite the significance of testing in epidemic control, the recent literature on the subject lacks a control-theoretic perspective. In this paper, an epidemic model is proposed that incorporates the testing rate as a control input and differentiates the undetected infected from the detected infected cases, who are assumed to be removed from the disease spreading process in the population. After estimating the model on the data corresponding to the beginning phase of COVID-19 in France, two testing policies are proposed: the so-called best-effort strategy for testing (BEST) and constant optimal strategy for testing (COST). The BEST policy is a suppression strategy that provides a minimum testing rate that stops the growth of the epidemic when implemented. The COST policy, on the other hand, is a mitigation strategy that provides an optimal value of testing rate minimizing the peak value of the infected population when the total stockpile of tests is limited. Both testing policies are evaluated by their impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths for the COVID-19 case of France.
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Submitted on : Sunday, September 26, 2021 - 12:42:49 PM
Last modification on : Thursday, April 7, 2022 - 1:58:32 PM

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Muhammad Umar Niazi, Alain Kibangou, Carlos Canudas de Wit, Denis Nikitin, Liudmila Tumash, et al.. Modeling and Control of Epidemics through Testing Policies. Annual Reviews in Control, Elsevier, 2021, 52, pp.554-572. ⟨10.1016/j.arcontrol.2021.09.004⟩. ⟨hal-02986566v2⟩

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