<p>This study presents a fractional-order model to investigate the impact of human papillomavirus (HPV) on the progression of cervical cancer, aiming to provide a comprehensive mathematical framework. The classical integer-order model is restructured using the Atangana-Baleanu Caputo operator, which introduces fractional calculus into the disease dynamics. The population under study is classified into four key groups: susceptible individuals, HPV-infected individuals, cervical cancer-infected individuals, and those who have recovered. To establish the model’s mathematical integrity, the positivity and boundedness properties are evaluated using the Mittag-Leffler function and Laplace transforms. Key epidemiological quantities, such as the basic reproductive number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2243_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and the strength number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2243_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {A}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">A</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, are derived by employing the next-generation matrix approach. To gain deeper insights into the model’s accuracy, sensitivity analysis was conducted to analyze the impact of involved parameters on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2243_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. Both disease-free and endemic equilibria are examined in terms of their local and global stability. Fixed point theory is used to demonstrate the existence and uniqueness of solutions to the model. In addition to the theoretical insights, the Toufik-Atangana numerical method is applied to simulate the model, providing an approximation that supports the analytical findings. The numerical results highlight the importance of fractional-order derivatives in understanding the complex dynamics of disease transmission. The study underscores the significance of reducing the contact rate as an effective strategy to limit the transmission of HPV and curb the spread of cervical cancer.</p>

Numerical analysis of HPV and its association with cervical cancer using Atangana–Baleanu fractional derivative

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发表日期：

2025年1月8日

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Nauman Raza,
Ali Raza,
Younes Chahlaoui,
J. F. Gomez-Aguilar

摘要

This study presents a fractional-order model to investigate the impact of human papillomavirus (HPV) on the progression of cervical cancer, aiming to provide a comprehensive mathematical framework. The classical integer-order model is restructured using the Atangana-Baleanu Caputo operator, which introduces fractional calculus into the disease dynamics. The population under study is classified into four key groups: susceptible individuals, HPV-infected individuals, cervical cancer-infected individuals, and those who have recovered. To establish the model’s mathematical integrity, the positivity and boundedness properties are evaluated using the Mittag-Leffler function and Laplace transforms. Key epidemiological quantities, such as the basic reproductive number $\mathcal {R}_0$ $R_{0}$ and the strength number $\mathcal {A}_0$ $A_{0}$ , are derived by employing the next-generation matrix approach. To gain deeper insights into the model’s accuracy, sensitivity analysis was conducted to analyze the impact of involved parameters on $\mathcal {R}_0$ $R_{0}$ . Both disease-free and endemic equilibria are examined in terms of their local and global stability. Fixed point theory is used to demonstrate the existence and uniqueness of solutions to the model. In addition to the theoretical insights, the Toufik-Atangana numerical method is applied to simulate the model, providing an approximation that supports the analytical findings. The numerical results highlight the importance of fractional-order derivatives in understanding the complex dynamics of disease transmission. The study underscores the significance of reducing the contact rate as an effective strategy to limit the transmission of HPV and curb the spread of cervical cancer.