Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative

Simphiwe M. Simelane; Justin B. Munyakazi; Phumlani G. Dlamini; Oluwaseun F. Egbelowo; Simphiwe M. Simelane; Justin B. Munyakazi; Phumlani G. Dlamini; Oluwaseun F. Egbelowo

doi:10.3934/mbe.2023515

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 11605-11626. doi: 10.3934/mbe.2023515

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Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative

1.
Department of Mathematics and Applied Mathematics, University of Johannesburg, Doornfontein, 2028, South Africa
2.
Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
3.
DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa

Academic Editor: Xiang-Sheng Wang

Received: 22 October 2022 Revised: 29 January 2023 Accepted: 02 February 2023 Published: 05 May 2023

We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer. First, we discuss the general structure of Caputo fractional derivatives and integrals. Next, we define the fractional HPV model using Caputo derivatives. The model equilibrium quantities, with their stability, are discussed based on the magnitude of the reproduction number. We compute and simulate numerical solutions of the presented fractional model using the Adams-Bashforth-Moulton scheme. Meanwhile, real data sourced from reports from the World Health Organization is used to establish the parameters and compute the basic reproduction number. We present figures of state variables for different fractional orders and the classical integer order. The impacts of vaccination and public health education are discussed through numerical simulations. From the results, we observe that an increase in both vaccination rates and public health education increases the quality of life, and thus, reduces disease burden and suffering in communities. The results also confirm that modeling HPV transmission dynamics using fractional derivatives includes history effects in the model, making the model further insightful and appropriate for studying HPV dynamics.
- human papillomavirus,
- cervical cancer,
- Adams-Bashforth-Moulton method,
- mean value theorem,
- Caputo fractional derivative,
- Routh-Hurwitz criterion
Citation: Simphiwe M. Simelane, Justin B. Munyakazi, Phumlani G. Dlamini, Oluwaseun F. Egbelowo. Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11605-11626. doi: 10.3934/mbe.2023515

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Abstract

We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer. First, we discuss the general structure of Caputo fractional derivatives and integrals. Next, we define the fractional HPV model using Caputo derivatives. The model equilibrium quantities, with their stability, are discussed based on the magnitude of the reproduction number. We compute and simulate numerical solutions of the presented fractional model using the Adams-Bashforth-Moulton scheme. Meanwhile, real data sourced from reports from the World Health Organization is used to establish the parameters and compute the basic reproduction number. We present figures of state variables for different fractional orders and the classical integer order. The impacts of vaccination and public health education are discussed through numerical simulations. From the results, we observe that an increase in both vaccination rates and public health education increases the quality of life, and thus, reduces disease burden and suffering in communities. The results also confirm that modeling HPV transmission dynamics using fractional derivatives includes history effects in the model, making the model further insightful and appropriate for studying HPV dynamics.

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