Article Sidebar

Submitted
Dec 28, 2021
Published
Dec 30, 2021
Download
pdf
Statistic
Read Counter : 0 Download : 0

Main Article Content

Abstract

Acute Respiratory Infection (ARI) is an infectious disease caused by bacteria and an unhealthy environment. The number of sufferers of this disease tends to increase and expand. The purpose of this study was to construct a mathematical model of the SEHAR epidemic (Suspectible-Exposed-Infected-Asthma-Recovered), analyze the stability of the equilibrium point and simulate the model. The results obtained are the SEHAR mathematical model for the spread of ARI disease which produces a disease-free equilibrium point and an endemic equilibrium point from the model. The method used is the stability analysis of the model using the Routh-Hurwitz Criteria to identify the characteristics of the eigenvalues. From the results of the stability analysis, it is found that the disease-free equilibrium point Eo and the endemic equilibrium point E1 are stable if the conditions for the relationship between parameters are met. At the end of the study, a simulation model was given using the Maple application

Keywords

Acute Respiratory Infection (ARI), SEHAR mathematical model, Routh-Hurwitz

Article Details

Author Biography

Nurfadilah

Assalamualaikum.

Saya telah submit artikel, mohon direview.

Terima kasih

References

  1. Antoon, H. 1995. Aljabar Linear Elementer Edisi ke-5. Terjemahan Pantur Silaban dan I Nyoman Susila. Jakarta. Erlangga.
  2. Boyce, W. E. dan R. C.Diprima. 2009. Elementary Differential Equation and Boundary Value Problem. Ninth Edition. John Wiley and Sons, Inc.USA
  3. Diekmann.O dan Heesterbee. J.A.P. 2000. Mathematical Epidemiology of Infectious Disease, John Wiley &Sons Ltd., Chicester.
  4. Drissche and Watmough. 2002. Reproduction Numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 180(2002).hlm. 29-48
  5. F. Dewi. 2017. Analisis Dinamik Model Penyebaran Virrus Influenza Dengan Resistensi Penyakit. Skripsi. Malang: Universitas Brawijaya
  6. Juliah, Intan. 2015. Analisis Kestabilan Titik Kesetimbangan Model Matematika Proses Transmisi Virus Dengue di dalam Tubuh Manusia dengan Terapi Obat Herbal, Semarang: Universitas Negeri Semarang.
  7. Jusrawati. 2018. Pemodelan Matematika Terhadap Kelangsungan Hidup Penderita Diabetes Melitus, Makassar: Universitas Islam Negeri (UIN) Alauddin.
  8. Kocak, H. and Hole, J.K. 1991. Dynamical and Bifurcation. New York: Springer-Verlag
  9. Kurniawan.B dkk. 2018. Membanguan Model Matematika Penyebaran Penyakit ISPA, Jurnal Matematika dan Terapan no.15.pp.36-47.januari.2018
  10. Nuryadi. 2018. Persamaan Diferensial Elementer. Yogyakarta: Media Pustaka
  11. Olsder. G.J. dkk. 1998. Mathematical System Theory Second Edition. Faculty On Information Technologhy and Sistem Deft Unoversity
  12. Pagalay. Usman. 2009. Mathematical Modeling (Aplikasi Pada Kedokteran Imunologi, Biologi, Ekonomi, Dan Perikanan).Malang.
  13. Palgunadi, Sarngadi. 2014. Simulasi Penyebaran Penyakit ISPA di Kota Surakarta Menggunakan Game Of Life. Surakarta: Universitas Sebelas Maret.
  14. Putri, R.T. 2016, Hubungan Merokok, Hipertendi, Diabetes Melitus dengan Penyakit Katarak pda Usia 40-60 Tahun di Kelurahan Siring Agung Palembang. Palembang: Universitas Muhammadiyah Palembang
  15. Ross, L. Shepley. 1987. Differential Equations 3th. New York: University of New Hapshire
  16. Wiggins, Stephen. 2003, Introduction to Applied Nonlinear Dynamical System and Chaos, Second Edition. New York: Springer-Verlag
  17. Yuliani, dkk. 2016. Analisis Penyebaran Penyakit Diare Sebagai Salah Satu Penyebab Kematian Blita Menggunakan Model Matematika SIS. Jurnal Matematika-S1,5(6),
  18. Yulida, Yuni., dan Karin, M.A. 2021. Model Matematika SEID (Susceptible, Exposed, Infected, Recovered dan Death) Untuk Penyebaran Penyakit ISPA. Skripsi. Universitas Lambung Mangkurat.