Hepatitis-B disease modelling of fractional order and parameter calibration using real data from the USA

Mehmet Yavuz; Kübra Akyüz; Naime Büşra Bayraktar; Feyza Nur Özdemir; Mehmet Yavuz; Kübra Akyüz; Naime Büşra Bayraktar; Feyza Nur Özdemir

doi:10.3934/biophy.2024021

AIMS Biophysics

2024, Volume 11, Issue 3: 378-402. doi: 10.3934/biophy.2024021

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Hepatitis-B disease modelling of fractional order and parameter calibration using real data from the USA

1.
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Meram Yeniyol, 42090 Konya, Türkiye
2.
Centre for Environmental Mathematics, Department of Earth and Environmental Sciences, University of Exeter-Penryn Campus, TR10 9FE, United Kingdom
3.
Department of Computer Engineering, Institute of Science, Necmettin Erbakan University, Meram Köyceğiz, 42090 Konya, Türkiye

Received: 20 July 2024 Revised: 20 September 2024 Accepted: 20 September 2024 Published: 29 September 2024

In this paper, a new mathematical model of Hepatitis B is studied to investigate the transmission dynamics of the Hepatitis B virus (HBV). Many diseases can start from the womb and find us humans throughout our lives. These diseases are specific abnormal conditions that negatively affect the structure or function of all or part of an organism and do not suddenly occur in any region due to external injury. In this study, we focus on HBV, and we state the graphics, interpretations, and detailed information about the disease and the newly established mathematical model of the disease. A fractional order differential equation system with a memory effect is used to model anomalous processes and to understand the effect of past infection events on the future spread dynamics of the system. In the model, susceptible, latent, acute, carrier, and recovered populations are taken into account by considering vertical transmission, which provides information about the inter-generational course of the disease. However, the migration effect is also used in the model due to the risk of disease transmission and increased migration in recent years. The course of the disease is examined using real data from the USA. Moreover, the model's positivity and boundedness are studied, and the equilibrium points are calculated. Additionally, the stability conditions for the disease-free equilibrium (DFE) are stated. A parameter calibration technique is used to determine the most accurate parameter values in the model. Finally, we provide numerical results and their biological interpretations to estimate the future course of the disease. The paper addresses the current migration problem with the migration parameter in the model. These differences from the literature can be regarded as important novelties of the paper.
- hepatitis-B (HBV),
- mathematical model of fractional-order,
- migration factor,
- real data,
- vertical transmission
Citation: Mehmet Yavuz, Kübra Akyüz, Naime Büşra Bayraktar, Feyza Nur Özdemir. Hepatitis-B disease modelling of fractional order and parameter calibration using real data from the USA[J]. AIMS Biophysics, 2024, 11(3): 378-402. doi: 10.3934/biophy.2024021

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Abstract

In this paper, a new mathematical model of Hepatitis B is studied to investigate the transmission dynamics of the Hepatitis B virus (HBV). Many diseases can start from the womb and find us humans throughout our lives. These diseases are specific abnormal conditions that negatively affect the structure or function of all or part of an organism and do not suddenly occur in any region due to external injury. In this study, we focus on HBV, and we state the graphics, interpretations, and detailed information about the disease and the newly established mathematical model of the disease. A fractional order differential equation system with a memory effect is used to model anomalous processes and to understand the effect of past infection events on the future spread dynamics of the system. In the model, susceptible, latent, acute, carrier, and recovered populations are taken into account by considering vertical transmission, which provides information about the inter-generational course of the disease. However, the migration effect is also used in the model due to the risk of disease transmission and increased migration in recent years. The course of the disease is examined using real data from the USA. Moreover, the model's positivity and boundedness are studied, and the equilibrium points are calculated. Additionally, the stability conditions for the disease-free equilibrium (DFE) are stated. A parameter calibration technique is used to determine the most accurate parameter values in the model. Finally, we provide numerical results and their biological interpretations to estimate the future course of the disease. The paper addresses the current migration problem with the migration parameter in the model. These differences from the literature can be regarded as important novelties of the paper.

Acknowledgments

This research was supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK) under the undergraduate research project.

Conflict of interest

Mehmet Yavuz is the Guest Editor of special issue “Importance of modelling and simulation in biophysical applications” for AIMS Biophysics. Mehmet Yavuz was not involved in the editorial review and the decision to publish this article. The authors declare that there is no conflict of interest.

Data Availability Statement

No Data associated in the manuscript.

Author contributions

Mehmet Yavuz conceptualized the study, designed the methodology, conducted data analysis, supervised the project, and contributed to writing and revising the manuscript. Kübra Akyüz assisted with the literature review, collected data, and contributed to writing and revising the manuscript. Naime Büşra Bayraktar assisted with the literature review, collected data, and contributed to writing and revising the manuscript. Feyza Nur Özdemir assisted with the literature review, collected data, and contributed to writing and revising the manuscript.

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