Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy

Infectious diseases have been one of the major causes of human mortality, and mathematical models have been playing significant roles in understanding the spread mechanism and controlling contagious diseases. In this paper, we propose a delayed SEIR epidemic model with intervention strategies and re...

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Autores principales:	Sarita Bugalia, Jai Prakash Tripathi, Hao Wang
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	basic reproduction number stability local hopf bifurcation global hopf bifurcation nyquist criterion stability switching curves Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1dbae7def7484dfeaa784dd86ddbe4f4
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spelling	oai:doaj.org-article:1dbae7def7484dfeaa784dd86ddbe4f42021-11-09T05:52:04ZMathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy10.3934/mbe.20212951551-0018https://doaj.org/article/1dbae7def7484dfeaa784dd86ddbe4f42021-06-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021295?viewType=HTMLhttps://doaj.org/toc/1551-0018Infectious diseases have been one of the major causes of human mortality, and mathematical models have been playing significant roles in understanding the spread mechanism and controlling contagious diseases. In this paper, we propose a delayed SEIR epidemic model with intervention strategies and recovery under the low availability of resources. Non-delayed and delayed models both possess two equilibria: the disease-free equilibrium and the endemic equilibrium. When the basic reproduction number R0=1, the non-delayed system undergoes a transcritical bifurcation. For the delayed system, we incorporate two important time delays: τ1 represents the latent period of the intervention strategies, and τ2 represents the period for curing the infected individuals. Time delays change the system dynamics via Hopf-bifurcation and oscillations. The direction and stability of delay induced Hopf-bifurcation are established using normal form theory and center manifold theorem. Furthermore, we rigorously prove that local Hopf bifurcation implies global Hopf bifurcation. Stability switching curves and crossing directions are analyzed on the two delay parameter plane, which allows both delays varying simultaneously. Numerical results demonstrate that by increasing the intervention strength, the infection level decays; by increasing the limitation of treatment, the infection level increases. Our quantitative observations can be useful for exploring the relative importance of intervention and medical resources. As a timing application, we parameterize the model for COVID-19 in Spain and Italy. With strict intervention policies, the infection numbers would have been greatly reduced in the early phase of COVID-19 in Spain and Italy. We also show that reducing the time delays in intervention and recovery would have decreased the total number of cases in the early phase of COVID-19 in Spain and Italy. Our work highlights the necessity to consider the time delays in intervention and recovery in an epidemic model.Sarita BugaliaJai Prakash TripathiHao WangAIMS Pressarticlebasic reproduction numberstabilitylocal hopf bifurcationglobal hopf bifurcationnyquist criterionstability switching curvesBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 5865-5920 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	basic reproduction number stability local hopf bifurcation global hopf bifurcation nyquist criterion stability switching curves Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	basic reproduction number stability local hopf bifurcation global hopf bifurcation nyquist criterion stability switching curves Biotechnology TP248.13-248.65 Mathematics QA1-939 Sarita Bugalia Jai Prakash Tripathi Hao Wang Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
description	Infectious diseases have been one of the major causes of human mortality, and mathematical models have been playing significant roles in understanding the spread mechanism and controlling contagious diseases. In this paper, we propose a delayed SEIR epidemic model with intervention strategies and recovery under the low availability of resources. Non-delayed and delayed models both possess two equilibria: the disease-free equilibrium and the endemic equilibrium. When the basic reproduction number R0=1, the non-delayed system undergoes a transcritical bifurcation. For the delayed system, we incorporate two important time delays: τ1 represents the latent period of the intervention strategies, and τ2 represents the period for curing the infected individuals. Time delays change the system dynamics via Hopf-bifurcation and oscillations. The direction and stability of delay induced Hopf-bifurcation are established using normal form theory and center manifold theorem. Furthermore, we rigorously prove that local Hopf bifurcation implies global Hopf bifurcation. Stability switching curves and crossing directions are analyzed on the two delay parameter plane, which allows both delays varying simultaneously. Numerical results demonstrate that by increasing the intervention strength, the infection level decays; by increasing the limitation of treatment, the infection level increases. Our quantitative observations can be useful for exploring the relative importance of intervention and medical resources. As a timing application, we parameterize the model for COVID-19 in Spain and Italy. With strict intervention policies, the infection numbers would have been greatly reduced in the early phase of COVID-19 in Spain and Italy. We also show that reducing the time delays in intervention and recovery would have decreased the total number of cases in the early phase of COVID-19 in Spain and Italy. Our work highlights the necessity to consider the time delays in intervention and recovery in an epidemic model.
format	article
author	Sarita Bugalia Jai Prakash Tripathi Hao Wang
author_facet	Sarita Bugalia Jai Prakash Tripathi Hao Wang
author_sort	Sarita Bugalia
title	Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
title_short	Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
title_full	Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
title_fullStr	Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
title_full_unstemmed	Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
title_sort	mathematical modeling of intervention and low medical resource availability with delays: applications to covid-19 outbreaks in spain and italy
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/1dbae7def7484dfeaa784dd86ddbe4f4
work_keys_str_mv	AT saritabugalia mathematicalmodelingofinterventionandlowmedicalresourceavailabilitywithdelaysapplicationstocovid19outbreaksinspainanditaly AT jaiprakashtripathi mathematicalmodelingofinterventionandlowmedicalresourceavailabilitywithdelaysapplicationstocovid19outbreaksinspainanditaly AT haowang mathematicalmodelingofinterventionandlowmedicalresourceavailabilitywithdelaysapplicationstocovid19outbreaksinspainanditaly
_version_	1718441275010580480

Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy

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