https://doi.org/10.1140/epjp/s13360-023-04287-5
Regular Article
A dynamical study of diarrhea delayed epidemic model: application of mathematical biology in infectious diseases
1
Department of Mathematics, Air University Islamabad, Islamabad, Pakistan
2
Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College, Wazirabad, Higher Education Department (HED), 54000, Lahore, Pakistan
3
Department of Mathematics, Science Faculty, Firat University, 23119, Elizig, Turkey
4
Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
5
Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, 54000, Lahore, Pakistan
6
Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey
7
Department of Mathematics and Statistics, The University of Lahore, 54590, Lahore, Pakistan
8
Department of H&BS, Military College of Signals, NUST, Islamabad, Pakistan
9
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
d
minc@firat.edu.tr
f
nauman.ahmed@math.uol.edu.pk
Received:
2
June
2023
Accepted:
16
July
2023
Published online:
29
July
2023
This manuscript presents the stability analysis of the diarrhea epidemic model with the effect of time delay. The delayed epidemic model for the disease of diarrhea contains four compartments, including susceptible, infective, treated, and recovered classes. The artificial delay parameter is designed with a saturated incidence rate of the model. The mathematical analysis is carried out by studying the equilibria, positivity, boundedness, and reproduction number for the said model. Furthermore, the sensitivity of the parameters is studied to strengthen the mathematical analysis. The diarrhea epidemic model's local and global stabilities are investigated using the acknowledged results of the Routh Hurwitz criterion and Lyapunov function, respectively. Moreover, the numerical results are obtained to support the analysis.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 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.
