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Efficiency of Protection in the Presence of Immigration Process for an Age-Structured Epidemiological Model

Efficiency of Protection in the Presence of Immigration Process for an Age-Structured... This paper studies the efficiency of protection in containing an epidemic in the case of immigration using a triple age structured model. For determining this efficiency, we split our study into two different cases, (i) with immigration flow into all model classes, (ii) without infected immigrants flow. For (i), we prove that the investigated model has no threshold dynamics and the infection always persists and the unique endemic equilibrium is globally stable. For (ii), we prove that by stopping the infected immigration flow, we obtain the threshold dynamics again. Therefore, we confirm that the infected immigration flow is responsible for eliminating the threshold dynamics. The global stability results in each case are shown with the help of the Lyapunov method. Some graphical representations are used to confirm the obtained results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Efficiency of Protection in the Presence of Immigration Process for an Age-Structured Epidemiological Model

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References (25)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-023-00572-8
Publisher site
See Article on Publisher Site

Abstract

This paper studies the efficiency of protection in containing an epidemic in the case of immigration using a triple age structured model. For determining this efficiency, we split our study into two different cases, (i) with immigration flow into all model classes, (ii) without infected immigrants flow. For (i), we prove that the investigated model has no threshold dynamics and the infection always persists and the unique endemic equilibrium is globally stable. For (ii), we prove that by stopping the infected immigration flow, we obtain the threshold dynamics again. Therefore, we confirm that the infected immigration flow is responsible for eliminating the threshold dynamics. The global stability results in each case are shown with the help of the Lyapunov method. Some graphical representations are used to confirm the obtained results.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Jun 1, 2023

Keywords: Age structured SPI model; Lyapunov functional; Uniform persistence; Total trajectory; Epidemiology; Immigration flow

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