PENGGUNAAN MODEL EPIDEMI SIR (SUSCEPTIBLES-INFECTED-REMOVED) PADA PENYEBARAN PENYAKIT HIV/AIDS DI MAKASSAR

Authors

  • Muhammad Rais Ridwan STKIP YPUP MAKASSAR
  • Fardinah Fardinah STKIP YPUP Makassar

DOI:

https://doi.org/10.24252/msa.v6i2.6201

Abstract

Penelitian ini menggunakan data jumlah penduduk Kota Makassar dan jumlah individu yang terinfeksi penyakit HIV/AIDS mulai tahun 2014 s.d 2016 diperoleh model penyebaran penyakit HIV/AIDS dengan penggunaan model epidemi SIR dengan titik ekuilibrium (S,I)=(15625,14276795).  Kemudian berdasarkan nilai eigen matriks Jacobi diperoleh titik (S,I) tersebut bersifat stabil asimtotik dengan nilai – nilai eigen -0,01 dan -91,4. Selanjutnya, diperoleh bilangan reproduksi dasar, yakni 91,471 yang menunjukkan bahwa satu individu yang terinfeksi, rata-rata dapat menularkan kepada 91 hingga 92 jiwa individu rentan terhadap penyakit HIV/AIDS. Dalam hal ini, penyakit tersebut di Kota Makassar akan bersifat endemik dalam kurun waktu 100 tahun ke depan. Hal ini dibuktikan dengan simulasi numerik menggunakan software Maple dan Matlab dengan melihat perilaku solusi penyelesaian S(t) dan I(t) untuk kurun waktu  yang relatif lama.

Author Biographies

Muhammad Rais Ridwan, STKIP YPUP MAKASSAR

Dosen Diperbantukan Kopertis (DPK) pada Program Studi Pendidikan Matematika STKIP YPUP Makassar

Fardinah Fardinah, STKIP YPUP Makassar

Pendidikan Matematika

References

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[5] Tang, Y., Huang, D., Ruan, S. and Zhang, W. 2008. “Coexistence of limit cycles and homoclinic loops in a SIRS model with a nonlinear infection forces”. SIAM J. Appl. Math., 69, 621-639.
[6] Tjolleng, A., Komalig, H.A.H, dan Prang, J.D. 2006. “Dinamika Perkembangan HIV/AIDS di Sulawesi Utara Menggunakan Model Persamaan Diferensial Nonlinear SIR (Susceptible, Infectious, and Recovered)”. Jurnal Ilmiah Sains, Vol. 13 N, 9-14.
[7] Xiao, D., and Ruan, S. 2007. “Global analysis of an epidemic model with nonmonotone incidence rate”. Math. Biosci, 208, 419-429.
[8] Zhixing, H., Ping, B., Wanbio, M., and Ruan, S. 2011. “Bifurcations of an SIRS epidemic model with nonlinear incidence rate”. Discrete Contin. Dyn. Syst. Ser. B, 2, 93-112.

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Published

2019-05-23

How to Cite

[1]
M. R. Ridwan and F. Fardinah, “PENGGUNAAN MODEL EPIDEMI SIR (SUSCEPTIBLES-INFECTED-REMOVED) PADA PENYEBARAN PENYAKIT HIV/AIDS DI MAKASSAR”, MSA, vol. 6, no. 2, pp. 1–7, May 2019.

Issue

Vol. 6 No. 2 (2018)

Section

Artikel

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