State estimation of the time-space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model.

Tello, Ivan F Y; Vande wouwer, Alain; Coutinho Daniel

doi:10.1016/j.jprocont.2022.08.016

Article (Scientific journals)

State estimation of the time-space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model.

Tello, Ivan F Y; Vande wouwer, Alain; Coutinho Daniel

2022 • In Journal of Process Control, 118, p. 231 - 241

Peer Reviewed verified by ORBi

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https://hdl.handle.net/20.500.12907/45105

DOI
10.1016/j.jprocont.2022.08.016

PubMed
36118074

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Keywords :

Epidemiological models; Linear matrix inequalities; Observer; State estimation; Sum of squares; Distributed-parameter; Epidemiological modeling; Linear matrix in equalities; Observer-based; Real-time estimation; Real-time prediction; Space propagation; Sums of squares; Time-space; Control and Systems Engineering; Modeling and Simulation; Computer Science Applications; Industrial and Manufacturing Engineering

Abstract :

[en] The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time-space propagation of such diseases using a diffusion-reaction epidemiological model of the susceptible-exposed-infected-recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Tello, Ivan F Y ; Universidad Tecnológica del Perú, Lima, Perú ; Department of Engineering, Mechatronics Section, Pontificia Universidad Católica del Perú, Lima, Perú

Vande wouwer, Alain ^✱; Université de Mons - UMONS > Faculté Polytechnique > Service Systèmes, Estimation, Commande et Optimisation

Coutinho Daniel; Federal University of Santa Catarina, Brazil > Postgraduate Program in Engineering of Automation and Systems

^✱ These authors have contributed equally to this work.

Language :

English

Title :

State estimation of the time-space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model.

Publication date :

October 2022

Journal title :

Journal of Process Control

ISSN :

0959-1524

Publisher :

Elsevier Ltd, England

Volume :

118

Pages :

231 - 241

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0959152422001585?httpAccept=text/xml

Research institute :

R100 - Institut des Biosciences

Available on ORBi UMONS :

since 17 January 2023

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Bibliography

Kermack, W.O., McKendrick, A.G., A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A, Containing Pap. Math. Phys. Character 115:772 (1927), 700–721.
Keeling, M.J., Rohani, P., Modeling Infectious Diseases in Humans and Animals. 2011, Princeton University Press.
Brauer, F., Castillo-Chavez, C., Feng, Z., Mathematical Models in Epidemiology, Vol. 32. 2019, Springer.
Makhoul, M., Ayoub, H.H., Chemaitelly, H., Seedat, S., Mumtaz, G.R., Al-Omari, S., Abu-Raddad, L.J., Epidemiological impact of SARS-CoV-2 vaccination: Mathematical modeling analyses. Vaccines, 8(4), 2020, 668.
Chen, N., Zhou, M., Dong, X., Qu, J., Gong, F., Han, Y., Qiu, Y., Wang, J., Liu, Y., Wei, Y., et al. Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: A descriptive study. Lancet 395:10223 (2020), 507–513.
Ndaïrou, F., Area, I., Nieto, J.J., Torres, D.F., Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan. Chaos Solitons Fractals, 135, 2020, 109846.
Mammeri, Y., A reaction-diffusion system to better comprehend the unlockdown: Application of SEIR-type model with diffusion to the spatial spread of COVID-19 in France. 2020 arXiv preprint arXiv:2005.03499.
Blima, P.-A., Efimo, D., Ushirobir, R., A class of nonlinear adaptive observers for SIR epidemic model. 2018 European Control Conference, ECC, 2018, IEEE, 1–6.
Bliman, P.-A., Barros, B.D., Interval observers for SIR epidemic models subject to uncertain seasonality. International Symposium on Positive Systems, 2016, Springer, 31–39.
Aronna, M.S., Bliman, P.-A., Interval observer for uncertain time-varying SIR-SI model of vector-borne disease. 2017.
Doussin, B., Adam, C., Georges, D., Combining SIR and agent-based models of the COVID-19 epidemics. GAMA Days 2021, 2021.
Shamil, M., Farheen, F., Ibtehaz, N., Khan, I.M., Rahman, M.S., et al. An agent-based modeling of COVID-19: Validation, analysis, and recommendations. Cognit. Comput., 2021, 1–12.
Rajaei, A., Raeiszadeh, M., Azimi, V., Sharifi, M., State estimation-based control of COVID-19 epidemic before and after vaccine development. J. Process Control 102 (2021), 1–14.
Chen, D., Yang, Y., Zhang, Y., Yu, W., Prediction of COVID-19 spread by sliding mSEIR observer. Sci. China Inf. Sci. 63:12 (2020), 1–13.
Martínez-Guerra, R., Flores-Flores, J.P., An algorithm for the robust estimation of the COVID-19 pandemic's population by considering undetected individuals. Appl. Math. Comput., 405, 2021, 126273.
Zemouche, A., Boutayeb, M., Bara, G.I., Observer design for nonlinear systems: An approach based on the differential mean value theorem. Proceedings of the 44th IEEE Conference on Decision and Control, 2005, IEEE, 6353–6358.
Adams, R., Sobolev Spaces. 1978, Academic Press. Inc.
Payne, L.E., Weinberger, H.F., An optimal Poincaré inequality for convex domains. Arch. Ration. Mech. Anal. 5:1 (1960), 286–292.
Arcede, J.P., Caga-anan, R.L., Mentuda, C.Q., Mammeri, Y., Accounting for symptomatic and asymptomatic in a SEIR-type model of COVID-19. 2020 arXiv preprint arXiv:2004.01805.
Lauer, S.A., Grantz, K.H., Bi, Q., Jones, F.K., Zheng, Q., Meredith, H.R., Azman, A.S., Reich, N.G., Lessler, J., The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: Estimation and application. Ann. Internal Med. 172:9 (2020), 577–582.
Liu, Z., Magal, P., Seydi, O., Webb, G., Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data. 2020 arXiv preprint arXiv:2002.12298.
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory. 1994, SIAM.
Khalil, H.K., Nonlinear Systems. third ed., 2002, Prentice Hall.
Papachristodoulou, A., Anderson, J., Valmorbida, G., Prajna, S., Seiler, P., Parrilo, P.A., Sum of squares optimization toolbox for MATLAB user's guide. 2013.