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Modeling and Control of COVID-19 Epidemic 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 NECS-POST - Systèmes Commandés en Réseau
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 for the infected cases is one of the most important mechanisms to control an epidemic. It enables to isolate the detected infected individuals, thereby limiting the disease transmission to the susceptible population. However, despite the significance of testing policies, the recent literature on the subject lacks a control-theoretic perspective. In this work, an epidemic model that incorporates the testing rate as a control input is presented. The proposed model differentiates the undetected infected from the detected infected cases, who are assumed to be removed from the disease spreading process in the population. First, the model is estimated and validated for COVID-19 data in France. Then, 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 lower bound on the testing rate such that the epidemic switches from a spreading to a non-spreading state. The COST policy is a mitigation strategy that provides an optimal value of testing rate that minimizes the peak value of the infected population when the total stockpile of tests is limited. Both testing policies are evaluated by predicting the number of active intensive care unit (ICU) cases and the cumulative number of deaths due to COVID-19.
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Contributor : Muhammad Umar B. Niazi <>
Submitted on : Tuesday, November 3, 2020 - 10:02:40 AM
Last modification on : Wednesday, June 2, 2021 - 4:27:10 PM
Long-term archiving on: : Thursday, February 4, 2021 - 6:13:02 PM


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  • HAL Id : hal-02986566, version 1
  • ARXIV : 2010.15438


Muhammad Umar Niazi, Alain Kibangou, Carlos Canudas de Wit, Denis Nikitin, Liudmila Tumash, et al.. Modeling and Control of COVID-19 Epidemic through Testing Policies. 2020. ⟨hal-02986566⟩



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