Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay

Based on the SIQR model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed SIQR...

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Autores principales:	Shishi Wang, Yuting Ding, Hongfan Lu, Silin Gong
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	covid-19 epidemic model time delay hopf bifurcation normal form multiple time scales Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b305a294727e4a0cac3dcf1351f963e3
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id	oai:doaj.org-article:b305a294727e4a0cac3dcf1351f963e3
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spelling	oai:doaj.org-article:b305a294727e4a0cac3dcf1351f963e32021-11-09T02:18:38ZStability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay10.3934/mbe.20212781551-0018https://doaj.org/article/b305a294727e4a0cac3dcf1351f963e32021-06-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021278?viewType=HTMLhttps://doaj.org/toc/1551-0018Based on the SIQR model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed SIQR model. Second, we analyze the existence of Hopf bifurcations associated with two equilibria, and we verify that Hopf bifurcations occur as delays crossing some critical values. Then, we derive the normal form for Hopf bifurcation by using the multiple time scales method for determining the stability and direction of bifurcation periodic solutions. Finally, numerical simulations are carried out to verify the analytic results.Shishi WangYuting Ding Hongfan Lu Silin GongAIMS Pressarticlecovid-19 epidemic modeltime delayhopf bifurcationnormal formmultiple time scalesBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 5505-5524 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	covid-19 epidemic model time delay hopf bifurcation normal form multiple time scales Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	covid-19 epidemic model time delay hopf bifurcation normal form multiple time scales Biotechnology TP248.13-248.65 Mathematics QA1-939 Shishi Wang Yuting Ding Hongfan Lu Silin Gong Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay
description	Based on the SIQR model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed SIQR model. Second, we analyze the existence of Hopf bifurcations associated with two equilibria, and we verify that Hopf bifurcations occur as delays crossing some critical values. Then, we derive the normal form for Hopf bifurcation by using the multiple time scales method for determining the stability and direction of bifurcation periodic solutions. Finally, numerical simulations are carried out to verify the analytic results.
format	article
author	Shishi Wang Yuting Ding Hongfan Lu Silin Gong
author_facet	Shishi Wang Yuting Ding Hongfan Lu Silin Gong
author_sort	Shishi Wang
title	Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay
title_short	Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay
title_full	Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay
title_fullStr	Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay
title_full_unstemmed	Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay
title_sort	stability and bifurcation analysis of siqr for the covid-19 epidemic model with time delay
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/b305a294727e4a0cac3dcf1351f963e3
work_keys_str_mv	AT shishiwang stabilityandbifurcationanalysisofsiqrforthecovid19epidemicmodelwithtimedelay AT yutingding stabilityandbifurcationanalysisofsiqrforthecovid19epidemicmodelwithtimedelay AT hongfanlu stabilityandbifurcationanalysisofsiqrforthecovid19epidemicmodelwithtimedelay AT silingong stabilityandbifurcationanalysisofsiqrforthecovid19epidemicmodelwithtimedelay
_version_	1718441413960531968

Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay

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