Version 1
: Received: 22 October 2024 / Approved: 22 October 2024 / Online: 22 October 2024 (10:28:44 CEST)
How to cite:
Villafuerte Segura, R.; Ochoa Ortega, G.; Hernández Ávila, J. A.; Ramirez Neria, M. State Observer for Time-Delay Systems Applied a Sir Compartmental Epidemiological Model for the COVID-19. Preprints2024, 2024101706. https://doi.org/10.20944/preprints202410.1706.v1
Villafuerte Segura, R.; Ochoa Ortega, G.; Hernández Ávila, J. A.; Ramirez Neria, M. State Observer for Time-Delay Systems Applied a Sir Compartmental Epidemiological Model for the COVID-19. Preprints 2024, 2024101706. https://doi.org/10.20944/preprints202410.1706.v1
Villafuerte Segura, R.; Ochoa Ortega, G.; Hernández Ávila, J. A.; Ramirez Neria, M. State Observer for Time-Delay Systems Applied a Sir Compartmental Epidemiological Model for the COVID-19. Preprints2024, 2024101706. https://doi.org/10.20944/preprints202410.1706.v1
APA Style
Villafuerte Segura, R., Ochoa Ortega, G., Hernández Ávila, J. A., & Ramirez Neria, M. (2024). State Observer for Time-Delay Systems Applied a Sir Compartmental Epidemiological Model for the COVID-19. Preprints. https://doi.org/10.20944/preprints202410.1706.v1
Chicago/Turabian Style
Villafuerte Segura, R., Jorge Antonio Hernández Ávila and Mario Ramirez Neria. 2024 "State Observer for Time-Delay Systems Applied a Sir Compartmental Epidemiological Model for the COVID-19" Preprints. https://doi.org/10.20944/preprints202410.1706.v1
Abstract
In this paper a Luenberger-type state observer for a class of nonlinear systems with multiple delays is presented. Sufficient conditions are provided to guarantee practical stability of the error dynamics. An exponential decay of the observation error dynamics is assured using Lyapunov-Krasovskii functionals and the feasibility of Linear Matrix Inequalities. Also, a time-delay SIR compartmental epidemiological model is presented. Time delay corresponds to the transition rates between compartments. The model considers that a part of the recovered population becomes susceptible again after a period following recovery. Three time-delays are incorporated due to the exchange of individuals between the population compartments: $\tau_{1,2,3}$, for the dead-times of recovery, immunity loss and incubation, respectively. It is shown that the effective reproduction number of the delay model depends on the rate of the susceptible population which became infected but after a period starts to be infectious and the fraction of the infectious recovered after a time-delay. For the resulting delay model, the problem of state estimation is addressed. To illustrate the efficiency and performance of the proposed observer, we apply the developed results to the COVID-19 pandemic. The observer can estimate the compartmental populations of Susceptible $S(t)$ and Recovered $R(t)$ from only the availability of real data of the Infectious compartmental population $I_r(t)$. The $I_r(t)$ confirmed data used for the state estimation are from a 55-day window with the highest impact on the Mexican population, as reported by the World Health Organization (WHO).
Keywords
COVID-19; Luenberger-type state observer; SIR epidemiological model; Time delay systems
Subject
Computer Science and Mathematics, Mathematical and Computational Biology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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