https://doi.org/10.1140/epjp/s13360-024-05368-9
Regular Article
Modeling, analyzing and simulating the Measles transmission dynamics through efficient computational optimal control technique
1
Department of Mathematics, Government College University, Lahore, Pakistan
2
Department of Mathematics and Statistics, College of Science, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
3
Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, Pakistan
4
Department of Computer Science and Mathematics, Lebanese American University Beirut, Beirut, Lebanon
5
Department of Mathematics, Government Murray Graduate College, Sialkot, Pakistan
Received:
28
April
2024
Accepted:
16
June
2024
Published online:
1
July
2024
Measles is a global threat due to its high contagion and rapid spread, especially in low-vaccination areas. Despite advancements in vaccination programs, Measles outbreaks still occur. Cross-border transmission emphasizes the need for global immunization and collaboration to prevent resurgence of this disease. In this paper, our main goal is to be able to understand the transmission dynamics and control of Measles using an SVEITR model. Various fundamental properties of the model are established analytically such as existence of a unique, bounded and positive solution. We demonstrate the stability of the model at two main equilibria by imposing essential criteria to a threshold parameter, computed using next generation matrix method. We implement Non-Standard Finite Difference (NSFD) scheme to approximate solutions for the continuous system and validate our analytical results. With the goal of potentially eradicating the disease from the population, we evaluate the effectiveness of two control measures through simulations that remain constant over time and are tailored for both the susceptible and infected individuals. Sensitivity analysis is performed to identify responsive parameters. We introduce optimal control strategies by incorporating time-dependent vaccination and treatment, with the aim of minimizing infections, reducing disease severity, and improving public health. The novelty of the present work lies in employing NSFD scheme especially for optimal control problem solving, with the aim of managing and properly controlling the disease. This work not only enhances theoretical understanding but also provides practical insights for policymakers and public health officials striving to control and eradicate Measles globally. This motivation emphasizes the importance of the research in the context of public health, the innovative aspects of the methodology, and the potential practical applications of the findings.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
