# Mathematical Modeling of SEIR Type to Controlling Diabetes Mellitus Disease Using Insulin

• Asmaidi Asmaidi Program Studi Teknik Informatika, Politeknik Aceh Selatan
• Eka Dodi Suryanto Program Studi Teknik Informatika, Politeknik Aceh Selatan
Keywords: Diabetes Mellitus, mathematical modeling, fixed point, basic reproduction number, fixed point stability

### Abstract

In this research the developed model is SEIR type mathematical modeling using insulin as a form of treatment. SEIR is abbreviation of susceptible (S), exposed (E), infected (I) and recovered (R). Expected goals include to making mathematical models for spread of diabetes mellitus, fixed point determination and basic reproduction number, stability analysis of fixed point, simulation of fixed point stability, simulation of population behavior to know the strategy of controlling diabetes mellitus. Analytical and numerical analysis results were obtained two fixed points, namely the point of no disease (disease-free equilibrium) and the point of disease (endemic equilibrium). Stability analysis of each fixed point indicates that the fixed point there is no stable disease when R0 < 1, whereas the fixed point there is stable disease when R0 > 1. Numerical simulations show that, with reduced Susceptible population contact rate with the exposed population causing  to decrease, so the spread of the disease does not appear in the population. These results indicate that one strategy of controlling the spread of diabetes mellitus can be done by reducing the rate of contact susceptible population with eksposed.

### References

 Abraham dan San, R. 2015. Analisis Model Matematika Model Penyebaran Penyakit Diabetes Dengan Faktor Genetik. SAINS. 15(1)-31-37.

 Edelstein dan Keshet, L. 2005. Mathematical Models in Biology. Edisi 7. Random House. New York-USA.

 Jones. 2007. Note on R_0. Tesis. Department of Anthropological Sciences Stanford University, California.

 Kemenkes RI. 2014. Situasi dan Analisis Diabetes. Infodatin. Pusat Data dan Informasi Kementerian Kesehatan RI.

 Ngwa, G. A. Shu, W. S. 2000. A mathematical model for endemic malaria with variable human and mosquito populations. Math. Comput. Modelling. 32(2): 747-763.

 Trisnawati, S. K dan Setyorogo, S. 2013. Faktor Risiko Kejadian Diabetes Melitus Tipe II di Puskesmas Kecamatan Cengkareng Jakarta Barat Tahun 2012. Jurnal Ilmiah Kesehatan. 5(1).

 Ulfah, J. Kharis, M. Chotim, M. 2014. Model Matematika Untuk Penyakit Diabetes Mellitus Tanpa Faktor Genetik Dengan Perawatan. Unnes Journal of Mathematics. 3(1).

 van den Driessche, Watmough. 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 180(6): 29-48.
Published
2017-12-31
How to Cite

A. Asmaidi and E. D. Suryanto, “Mathematical Modeling of SEIR Type to Controlling Diabetes Mellitus Disease Using Insulin”, JI, vol. 2, no. 2, pp. 57-66, Dec. 2017.
Section
Articles