Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination

We consider a vaccination control into a age-structured susceptible-infective-recovered-susceptible (SIRS) model and study the global stability of the endemic equilibrium by the iterative method. The basic reproduction number $ R_0 $ is obtained. It is shown that if $ R_0 < 1 $, then the dise...

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Autores principales:	Han Ma, Qimin Zhang
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	sirs epidemic model age-structure threshold dynamics optional control hamilton-jacobi-bellman (hjb) equation Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/181b9b4ddfa54f5db904e652702d6d3d
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spelling	oai:doaj.org-article:181b9b4ddfa54f5db904e652702d6d3d2021-11-29T06:17:06ZThreshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination10.3934/mbe.20214651551-0018https://doaj.org/article/181b9b4ddfa54f5db904e652702d6d3d2021-10-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021465?viewType=HTMLhttps://doaj.org/toc/1551-0018We consider a vaccination control into a age-structured susceptible-infective-recovered-susceptible (SIRS) model and study the global stability of the endemic equilibrium by the iterative method. The basic reproduction number $ R_0 $ is obtained. It is shown that if $ R_0 < 1 $, then the disease-free equilibrium is globally asymptotically stable, if $ R_0 > 1 $, then the disease-free and endemic equilibrium coexist simultaneously, and the global asymptotic stability of endemic equilibrium is also shown. Additionally, the Hamilton-Jacobi-Bellman (HJB) equation is given by employing the Bellman's principle of optimality. Through proving the existence of viscosity solution for HJB equation, we obtain the optimal vaccination control strategy. Finally, numerical simulations are performed to illustrate the corresponding analytical results. Han MaQimin Zhang AIMS Pressarticlesirs epidemic modelage-structurethreshold dynamicsoptional controlhamilton-jacobi-bellman (hjb) equationBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 9474-9495 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	sirs epidemic model age-structure threshold dynamics optional control hamilton-jacobi-bellman (hjb) equation Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	sirs epidemic model age-structure threshold dynamics optional control hamilton-jacobi-bellman (hjb) equation Biotechnology TP248.13-248.65 Mathematics QA1-939 Han Ma Qimin Zhang Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
description	We consider a vaccination control into a age-structured susceptible-infective-recovered-susceptible (SIRS) model and study the global stability of the endemic equilibrium by the iterative method. The basic reproduction number $ R_0 $ is obtained. It is shown that if $ R_0 < 1 $, then the disease-free equilibrium is globally asymptotically stable, if $ R_0 > 1 $, then the disease-free and endemic equilibrium coexist simultaneously, and the global asymptotic stability of endemic equilibrium is also shown. Additionally, the Hamilton-Jacobi-Bellman (HJB) equation is given by employing the Bellman's principle of optimality. Through proving the existence of viscosity solution for HJB equation, we obtain the optimal vaccination control strategy. Finally, numerical simulations are performed to illustrate the corresponding analytical results.
format	article
author	Han Ma Qimin Zhang
author_facet	Han Ma Qimin Zhang
author_sort	Han Ma
title	Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
title_short	Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
title_full	Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
title_fullStr	Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
title_full_unstemmed	Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
title_sort	threshold dynamics and optimal control on an age-structured sirs epidemic model with vaccination
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/181b9b4ddfa54f5db904e652702d6d3d
work_keys_str_mv	AT hanma thresholddynamicsandoptimalcontrolonanagestructuredsirsepidemicmodelwithvaccination AT qiminzhang thresholddynamicsandoptimalcontrolonanagestructuredsirsepidemicmodelwithvaccination
_version_	1718407570839830528

Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination

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