Mathematical Models of Human Papillomavirus Transmission with Vaccination

Maria Lobo, Maria Machado, Waltrudis Adelia Asa

Abstract


The human papillomavirus (HPV) is one of the viruses that can cause cervical cancer. However, vaccination can prevent such a virus. The spread of the virus in cervical cancer can be modelled in the SI model, however, such a model has not produced accurate results. The development and extension of the model into S1S2IRC, with S1 denoting the population aged 0–10 years and S2 representing the population over 10 years, which is susceptible to HPV infection. The results produce disease-free and endemic equilibrium points. The analysis of the equilibrium points yields that the disease-free equilibrium point will be asymptotically stable for R0< 1 and R0 > 1 for the endemic equilibrium point. The results indicate that the higher the probability of humans being prone to the HPV virus, the greater the chance of these individuals being infected by the virus. Therefore, vaccination is required to protect against the virus infection.  

 


Keywords


mathematical modeling; human papillomavirus; cervical cancer

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References


[1] C. Marth, F. Landoni, S. Mahner, M. McCormack, A. Gonzalez-Martin, and N. Colombo, “Cervical cancer: ESMO Clinical Practice Guidelines for diagnosis, treatment, and follow-up,” Ann. Oncol., vol. 28, no. Supplement 4, pp. iv72–iv83, 2017, doi: 10.1093/annonc/mdx220.

[2] S. L. Lee and A. M. Tameru, “A mathematical model of human papillomavirus (HPV) in the United States and its impact on cervical cancer,” J. Cancer, vol. 3, no. 1, pp. 262–268, 2012, doi: 10.7150/jca.4161.

[3] J. N. I. Vet et al., “Prevalence of human papillomavirus in Indonesia: A population-based study in three regions,” Br. J. Cancer, vol. 99, no. 1, pp. 214–218, 2008, doi: 10.1038/sj.bjc.6604417.

[4] H. Nurhayati-Wollf, “Number of women screened for cervical cancer in Indonesia from 2015 to 2019,” Statista, p. 2022, 2019, [Online]. Available: https://www.statista.com/statistics/1084812/indonesia-cervical-cancer-screening/

[5] M. GUIVARC’H, “[Cervix uteri],” Quest. [d’internat], vol. 86, no. 445, pp. 1–10, 1962, doi: 10.1159/000429173.

[6] G. P. Garnett, J. J. Kim, K. French, and S. J. Goldie, “Chapter 21: Modelling the impact of HPV vaccines on cervical cancer and screening programmes.,” Vaccine, vol. 24 Suppl 3, p. S3/178-86, Aug. 2006, doi: 10.1016/j.vaccine.2006.05.116.

[7] G. Sroczynski et al., “Decision-analytic modeling to evaluate the long-term effectiveness and cost-effectiveness of HPV-DNA testing in primary cervical cancer screening in Germany.,” GMS Health Technol. Assess., vol. 6, no. April, p. Doc05, 2010, doi: 10.3205/hta000083.

[8] T. S. N. Asih, Widodo, L. Aryati, and F. A. Kusumo, “Cusp bifurcation on cervical cancer mathematical model,” J. Phys. Conf. Ser., vol. 1321, no. 2, 2019, doi: 10.1088/1742-6596/1321/2/022087.

[9] G. Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, and J. M. Hyman, “The basic reproduction number ℛ0 and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile,” Math. Biosci. Eng., vol. 10, no. 5–6, pp. 1455–1474, 2013, doi: 10.3934/mbe.2013.10.1455.

[10] K. T. Kristanti, T. Trisilowati, and A. Widodo, “Analisis Dinamik pada Model Kanker Serviks dengan Vaksinasi dan Screening,” Limits J. Math. Its Appl., vol. 17, no. 2, p. 157, 2020, doi: 10.12962/limits.v17i2.6901.

[11] K. Humolungo and R. Paudi, “Model Matematika Siuc Pada Kasus Kanker Serviks Dengan Vaksinasi,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 7, no. 1, pp. 32–36, 2019, doi: 10.34312/euler.v7i1.10331.

[12] P. Pongsumpun, “Mathematical Model of Cervical Cancer due to Human Papillomavirus Infection,” no. January, pp. 157–161, 2012.




DOI: https://doi.org/10.18860/ca.v9i1.25922

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