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Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic

The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investiga...

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Main Authors: Liu, Chongyang, Gao, Jie, Kanesan, Jeevan
Format: Article
Published: Springer 2024
Subjects:
QA Mathematics
QA75 Electronic computers. Computer science
Online Access:http://eprints.um.edu.my/45243/
https://doi.org/10.1186/s13660-024-03140-2
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spelling my.um.eprints.452432024-09-19T02:37:29Z http://eprints.um.edu.my/45243/ Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic Liu, Chongyang Gao, Jie Kanesan, Jeevan QA Mathematics QA75 Electronic computers. Computer science The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic. Springer 2024-05 Article PeerReviewed Liu, Chongyang and Gao, Jie and Kanesan, Jeevan (2024) Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic. Journal of Inequalities and Applications, 2024 (1). p. 66. ISSN 1029-242X, DOI https://doi.org/10.1186/s13660-024-03140-2 <https://doi.org/10.1186/s13660-024-03140-2>. https://doi.org/10.1186/s13660-024-03140-2 10.1186/s13660-024-03140-2
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
QA75 Electronic computers. Computer science
spellingShingle QA Mathematics
QA75 Electronic computers. Computer science
Liu, Chongyang
Gao, Jie
Kanesan, Jeevan
Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
description The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic.
format Article
author Liu, Chongyang
Gao, Jie
Kanesan, Jeevan
author_facet Liu, Chongyang
Gao, Jie
Kanesan, Jeevan
author_sort Liu, Chongyang
title Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
title_short Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
title_full Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
title_fullStr Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
title_full_unstemmed Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
title_sort dynamics analysis and optimal control of delayed seir model in covid-19 epidemic
publisher Springer
publishDate 2024
url http://eprints.um.edu.my/45243/
https://doi.org/10.1186/s13660-024-03140-2
_version_ 1811682107753234432
score 13.211869

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