Mathematical Model, Stability Analysis and Numerical Simulations for The Spread of Malaria Disease in Yogyakarta City, Indonesia


  • Prihantini Prihantini Institut Teknologi Bandung



Mathematical Model, SIDR, Stability Analysis


Indonesia merupakan negara yang sering terjadi penyakit malaria. Oleh karena itu, diperlukan model matematika yang mampu memodelkan distribusi malaria. Tujuan dari penelitian ini adalah untuk membuat model dengan variabel yang memperhatikan suspected, infeksi, dorman dan pulih. Hasil model yang terbentuk kemudian disimulasikan dengan menggunakan software maple 18. Dari hasil simulasi dapat disimpulkan bahwa terjadi penurunan populasi yang terinfeksi dan peningkatan populasi yang pulih dari waktu ke waktu.

[Indonesia is a country with frequent malaria cases. Therefore, a mathematical model is needed to model the distribution of malaria. The purpose of this study is to create a model with susceptible, infected, dormant and recovered compartments and to see the results of the simulation performed using maple 18 software. From the simulation results, it can be concluded that there is a decrease in the infected population and an increase in the recovered population over time.]


Download data is not yet available.

Author Biography

Prihantini Prihantini, Institut Teknologi Bandung

Department of Mathematics, Faculty of Mathematics and Science

References Accesed on November 03, 2021, 01.31 am. Accesed on November 03, 2021, 01.34 am.

Dhani Rhedono. Malaria Prevalence in Indonesia. Surakarta: Faculty of Medicine UNS. 2011.

Li, T. and Xue, Y. (2013) Global Stability Analysis of a Delayed SIDR Epidemic Model with Quarantine and Latent. Applied Mathematics, 4, 109-117.

Brachmant. (2002) Bioterrorism: An Update with a Focus on Malaria. America: American Journal of Epidemology, 155: 11.

Lahrouz, A., Omari, L., Kiouach, D. and Belmati, A. (2012) Complete Global Stability for an SIRS Epidemic Model with Generalized Non-Linear Incidence and Vaccination. Applied Mathematics and Computation, 218, 6519-6525.

Stein Z A and LaSalle J P 1979 The Stability of Dynamical Systems SIAM Journal on Applied Mathematics 21: 418-420

Li, M.Y. and Muldowney, J.S. (1996) A Geometric Approach to Global-Stability Problems. SIAM Journal on Mathematical Analysis, 27, 1070-1083.

Kalamas AG 2004 Anthrax Anesthesiology Clinics of North America 22: 533-540

Martin, R.H. (1974) Logarithmic Norms and Projections Applied to Linear Differential Systems. Journal of Mathematical Analysis and Applications, 45, 432-454.

Nuning Nuraini. Biological Mathematical Modeling. Bandung: Industry and Financial Mathematics Study Group Institute Technology of Bandung.

Perko, L. 1991. Differential Equation and Dynamical System. Springer-Verlag: New York.

Tasmanian hatred. (2014) Endemic SIR Model for Horizontal and Vertical Diseases. Surabaya: Proceedings of the XVII Mathematical National Conference, 9, 103-110

Widowati & Sutimin. 2007. Buku Ajar Pemodelan Matematika. Semarang: FMIPA UNDIP




How to Cite

Prihantini, P. (2021). Mathematical Model, Stability Analysis and Numerical Simulations for The Spread of Malaria Disease in Yogyakarta City, Indonesia. Jurnal Fourier, 10(2), 81–88.