Abstract
Human papillomavirus (HPV) is a prevalent virus that plays a significant role in develo** cervical cancer, a leading cause of cancer-related deaths among women worldwide. This study presents a novel fractional modeling approach for analyzing the transmission dynamics of HPV and its association with cervical cancer. The model incorporates different compartments to represent susceptible individuals, HPV-infected individuals, individuals with HPV and cervical cancer, and recovered individuals. We incorporate a Caputo fractional derivative in each model compartment to capture the long-term memory effect and non-local behavior in the disease progression. To examine the well-posedness of the model, we analyze the positivity and boundedness of the solutions. Additionally, we utilize the Banach fixed point theorem to establish the existence and uniqueness of the solution. We determine the infection-free and endemic equilibrium points and analyze their local stability. By constructing appropriate Lyapunov functions, the global stability of both equilibrium points is established based on the basic reproduction number \(\mathcal {R}_0\). The control parameter of the model is identified through a sensitivity analysis of \(\mathcal {R}_0\) using the forward sensitivity index. Finally, we utilize the Adams-Bashforth-Moulton method for numerical simulations to validate the theoretical results. The simulations verify that the long-term memory effect, characterized by the fractional order derivative, does not affect the stability of the equilibrium points. However, increasing the fractional order derivative leads to faster convergence of the solutions towards their respective equilibrium states. Also, these results reveal that implementing a vaccination program is an effective strategy for managing HPV transmission and cervical cancer.
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Acknowledgements
INSPIRE Fellowship (IF180053) under the Department of Science and Technology, Government of India, supports this research work to the first author, Mr. R. Praveen Kumar. We would like to express our gratitude to the reviewers for their detailed review and valuable feedback, which significantly contributed to the refinement of this manuscript.
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Praveen Kumar Rajan: Writing-Original draft preparation, Conceptualization, Software, Methodology, Formal analysis, Writing-Reviewing and Editing. Murugesan Kuppusamy: Supervision, Writing-Reviewing and Editing, Methodology. Abdullahi Yusuf: Software, Formal analysis and Methodology.
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Rajan, P.K., Kuppusamy, M. & Yusuf, A. A fractional-order modeling of human papillomavirus transmission and cervical cancer. Model. Earth Syst. Environ. 10, 1337–1357 (2024). https://doi.org/10.1007/s40808-023-01843-x
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DOI: https://doi.org/10.1007/s40808-023-01843-x
Keywords
- Human papillomavirus with cervical cancer
- Caputo fractional derivative
- Banach fixed point theory
- Adams–Bashforth–Moulton method