# MODEL MATEMATIKA KANKER NASOFARING DENGAN RADIOTERAPI

## (MATHEMATICAL MODEL OF NASOPHARYNX CANCER USING RADIOTHERAPY)

• Maulan Aziz Syafii Program Studi Matematika, Universitas Ahmad Dahlan, Yogyakarta, Indonesia

### Abstract

ABSTRACT. Nasopharyngeal carcinoma is a malignancy of the head and neck located in the nasopharynx. The disease is caused by infection with the Epstein-Barr virus (EBV). It is characterized by a unique set of geographic, etiological, and biological features that differ from other head and neck cancers. There are several ways to treat nasopharyngeal cancer, one of which is radiotherapy. In this study, a mathematical model of the development of nasopharyngeal cancer cells was formed in a system of ordinary differential equations with four variables describing the interactions between latent cells, infected cells, invasive carcinoma cells, and radiation. Furthermore, the analysis of the mathematical model, which includes the existence and local stability of the equilibrium point, is carried out. From the stability analysis, important parameters affect the conditions that cause cancer and the condition of being free of nasopharyngeal cancer. Numerical simulations were carried out to verify the results of the analysis that had been obtained.
Keywords: Nasopharyngeal cancer, mathematical model, stability of equilibria, simulation.

ABSTRAK. Karsinoma nasofaring atau kanker nasofaring (KNF) merupakan keganasan penyakit pada kepala dan leher yang terletak di nasofaring. Faktor risiko kanker nasofaring diantaranya adalah riwayat merokok, jenis kelamin, faktor nutrisi, faktor lingkungan, penggunaan alkohol, dan faktor genetik merupakan. Selain itu, infeksi virus, seperti virus Epstein-Barr, dapat menyebabkan kanker nasofaring. Salah satu cara penggobatan kanker nasofaring adalah dengan radioterapi. Pada penelitian ini dibentuk model matematika perkembangan sel kanker nasofaring dalam sistem persamaan diferensial biasa dengan empat variabel yang menggambarkan interaksi anatara sel laten, sel terinfeksi, sel Karsinoma invansif, dan radiasi. Selanjutnya dilakukan analisis model matematika yang meliputi eksistensi dan kestabilan lokal titik ekuilibrium. Dari analisis kestabilan diketahui parameter penting yang mempengaruhi kondisi penyebab kanker dan kondisi bebas kanker nasofaring. Simulasi numerik dilakukan untuk memverifikasi hasil analisis yang telah diperoleh.
Kata kunci: Kanker nasofaring, model matematika, kestabilan titik ekuilibrium, simulasi.

Published
2021-12-07
How to Cite
SYAFII, Maulan Aziz; ADI, Yudi Ari. MODEL MATEMATIKA KANKER NASOFARING DENGAN RADIOTERAPI. Jurnal Ilmiah Matematika dan Pendidikan Matematika, [S.l.], v. 13, n. 2, p. 13-26, dec. 2021. ISSN 2550-0422. Available at: <http://jos.unsoed.ac.id/index.php/jmp/article/view/4705>. Date accessed: 24 feb. 2024. doi: https://doi.org/10.20884/1.jmp.2021.13.2.4705.
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