Kestabilan Titik Ekuilibrium Endemik Pada Model SIS Transmisi Human Papillomavirus (HPV) Dengan Populasi Berbeda

Suryadi Harto Pratama; Irma Suryani; Wartono Wartono

doi:10.15575/kubik.v6i1.9189

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Suryadi Harto Pratama
UIN Sultan Syarif Kasim Riau
Indonesia

Irma Suryani
UIN Sultan Syarif Kasim Riau

Wartono Wartono
UIN Sultan Syarif Kasim Riau

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Kestabilan Titik Ekuilibrium Endemik Pada Model SIS Transmisi Human Papillomavirus (HPV) Dengan Populasi Berbeda

Suryadi Harto Pratama⁽¹⁾, Irma Suryani^(2*), Wartono Wartono⁽³⁾

(1) UIN Sultan Syarif Kasim Riau, Indonesia
(2) UIN Sultan Syarif Kasim Riau,
(3) UIN Sultan Syarif Kasim Riau,
(*) Corresponding Author

Abstract

Paper ini membahas model matematika tentang kestabilan titik ekuilibrium endemik terhadap Human Papillomavirus (HPV) pada model SIS dengan populasi berbeda. Model SIS Terdiri dari dua kompartemen, yaitu kompartemen rentan (Susceptible) dan kompartemen yang terinfeksi (Infected) dengan populasi yaitu subpopulasi perempuan dan subpopulasi laki-laki . Titik ekuilibrium endemik pada model SIS ini dapat dilakukan dengan melakukan substitusi atau manipulasi aljabar terhadap asumsi-asumsi pada model SIS Human Papillomavirus (HPV). Selanjutnya, kestabilan endemik dinyatakan stabil asimtotik dapat di uji menggunakan matriks Jacobian dengan syarat terpenuhi. Kemudian, model SIS Human Papillomavirus (HPV) dianalisis dengan simulasi numerik dengan hasil kestabilan titik ekuilibrium endemik itu stabil asimtotik jika . Dan ini menjelaskan bahwa subpopulasi terinfeksi akan memungkinkan menginfeksi atau menularkan virus kepada subpopulasi rentan. Artinya virus masih ada dalam populasi.

Keywords

Matriks Jacobian, model SIS, simulasi numerik, stabil asimtotik, titik ekuilibrium endemik.

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References

Nurhalimah, N., dkk, “Analisis Kestabilan Model Matematika SIA (Susceptible, Infected, AIDS Cases) untuk Penyakit AIDS”, Kubik: Jurnal Publikasi Ilmiah Matematika Vol. 3 No.1, pp. 83-87, 2018

Jevuska. “Penyakit Menular Seksual - Pengertian dan Sejenisnya”. https://www.jevuska.com/category/artikel-kedokteran/kulit (di akses tanggal 5 Desember 2019)

Barnabas, R.V. dkk. “Epidemiology of HPV 16 and Cervical Cancer in Finland and the Potential Impact of Vaccination: Mathematical Modelling Analyses''. Journal of Plos Medicine. 2006

Ribassin, L dan Majed. “A SIS Model for Human Papillomavirus Transmission”. Version 1. Villejuif: Journal Institut de Cancérologie Gustave Roussy. 2010

Driessche & Watmough. Reproduction Number and Subthreshold Endemic Equilibria for Compartmental Model of Disease Transmission. Mathematical Biosciences 18. Hal. 2. 2002

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Perko, L. “Differential Equations Dynamika System”. New York: Springer-Verlag. 1991

Grantmacher, F.H., Applications Of The Theory Matrices, Intersciences Publisher, New York, 1959

Suryani, I dan Asandi, A. “Kestabilan Global Titik Ekuilibrium Bebas Penyakit Pada Model SIS Transmisi Human Papillomavirus (HPV) dengan Populasi Berbeda”. Jurnal Sains Matematika dan Statistik. 2019

DOI: https://doi.org/10.15575/kubik.v6i1.9189

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Kestabilan Titik Ekuilibrium Endemik Pada Model SIS Transmisi Human Papillomavirus (HPV) Dengan Populasi Berbeda

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