Stability of Cervical Cancer Model by Human Papillomavirrus (HPV) with Migration

Irma Suryani, Mohammad Soleh, Wartono Wartono, Anggi Prayoga, Boby Fahlezi

Abstract


Cervical cancer is a chronic disease that attacks the cervix. This disease is caused by the human papillomavirus (HPV). Over time, cervical cancer is modeled with a mathematical model to describe the development of its spread. In this study, cervical cancer is modeled into four subpopulations; susceptible subpopulation (S), HPV-infected subpopulation (I), infected but not infected with cervical cancer (U) and infected and infected with cervical cancer (C). The SIUC model is then added to the existence of migration within the population. Furthermore, the equilibrium of the model is determine and its stability is analyzed using the Jacobian matrix and eigenvalues. The result is that there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The disease-free equilibrium point is asymptotically stable if the eigenvalue conditions are met. The endemic equilibrium point is stable if the eigenvalues are met. Furthermore, the numerical simulation model shows that migration that occurs within the population can cause cervical cancer to still exist in the population because the contact rate is getting bigger

Keywords


Eigen Values, Equilibrium, Jacobian Matrix, Model of Cervical Cancer SIUC

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References


A. Bastian, “Penerapan Algoritma K-Means Clustering Analysis pada Penyakit Menular Manusia (Studi Kasus Kabupaten Majalengka),” J. Sist. Inf., vol. 14, no. 1, pp. 28–34, 2018.

A. P. Sari and F. Syahrul, “Faktor yang Berhubungan Dengan Tindakan Vaksinasi HPV Pada Wanita Usia Dewasa,” J. Berk. Epidemiol., vol. 2, no. 3, pp. 321–330, 2014.

A. Yasmon, "Patogenesis Human Papillomavirus(HPV) pada Kanker Serviks," Jurnal Biotek Medisiana, vol. 8, no. 1, pp.23-32, 2019.

F. Utomo, A. Afandi, and S. B. Rivai, “Korelasi Durasi Penggunaan Kontrasepsi Oral Dan Stadium Kanker Serviks Di Rsud Arifin Achmad Provinsi Riau,” Collab. Med. J., vol. 3, no. 1, pp. 24–31, 2020, doi: 10.36341/cmj.v3i1.1126.

I. Suryani and A. Asandi, “Kestabilan Global Titik Ekuilibrium Bebas Penyakit Pada Model SIS Transmisi HUMAN PAPILLOMAVIRUS (HPV) Dengan Populasi Berbeda,” J. Sains Mat. dan Stat., vol. 5, no. 1, pp. 68–78, 2019.

Irma Suryani, Wartono, Suryadi Harto.P, "Kestabilan Titik Ekuilibrium Endemik Pada Model SIS Transmisi Human Papillomavirus (HPV) dengan Populasi Berbeda," Kubik: Jurnal Pubilkasi Ilmiah Matematika, vo. 6, no. 1, pp. 36-43, 2021.

J. Paavonen, “Human papillomavirus infection and the development of cervical cancer and related genital neoplasias,” Int. J. Infect. Dis., vol. 11, no. SUPPL. 2, 2007, doi: 10.1016/S1201-9712(07)60015-0.

L. Perko, Equations and Dynamical Systems. 2001.

N. Puspitasari, Y. A. Adi and R. S. Winanda, "Analisis Kestabilan Lokal pada Model Matematika Kanker Serviks Akibat Human Papillomavirus," Jurnal Ilmu Alam dan Teknologi Terapan, vol. 1, no. 1. pp.115-125, 2019.

R. V. Barnabas, P. Laukkanen, P. Koskela, O. Kontula, M. Lehtinen, and G. P. Garnett, “Epidemiology of HPV 16 and cervical cancer in Finland and the potential impact of vaccination: Mathematical modelling analyses,” PLoS Med., vol. 3, no. 5, pp. 624–632, 2006, doi: 10.1371/journal.pmed.0030138.

S.H.Strogatz, “Nonlinear dynamics and chaos,” Growing Explanations. pp. 65–66, 2020, doi: 10.1515/9780822390084-003.

L. Perko, Equations and Dynamical Systems. 2001.

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.

V. Nita and Novi Indrayani, “Pendidikan Kesehatan Dalam Upaya Pencegahan Kanker Serviks Pada Wanita Usia Subur,” Din. J. Pengabdi. Kpd. Masy., vol. 4, no. 2, pp. 306–310, 2020, doi: 10.31849/dinamisia.v4i2.4175.




DOI: http://dx.doi.org/10.30829/zero.v8i1.16137

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SLOT GACOR

SLOT GACOR

SLOT GACOR

SLOT GACOR

SLOT GACOR

SLOT GACOR

Department of Mathematics
Faculty of Science and Technology
Universitas Islam Negeri Sumatera Utara Medan 

Email: mtk.saintek@uinsu.ac.id

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