Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR

Authors

  • Willyam Daniel Sihotang Universitas Negeri Medan
  • Ceria Clara Simbolon Universitas Negeri Medan
  • July Hartiny Universitas Negeri Medan
  • Desrinawati Tindaon Universitas Negeri Medan
  • Lasker Pangarapan Sinaga Universitas Negeri Medan

DOI:

https://doi.org/10.20956/jmsk.v16i1.6594

Keywords:

Model of Measles, Stable Equilibrium Point, MR Vaccine

Abstract

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

References

Chasnov, Jeffrey R., 2009. Introduction to Differential Equations and Boundary Value Problems. JohnWiley and Sons., New York.

Dirjen P2PL., Kemenkes RI. 2013.Petunjuk Teknis Introduksi Imunisasi DPT-HB-Hib (Pentavalen) pada Bayi dan Pelaksanaan Imunisasi Lanjutan pada Anak Balita. Jakarta.

Kementerian Kesehatan RI., Situasi campak dan Rubella di Indonesia. Jakarta: Kementerian Kesehatan RI 2018.

Kholisoh S. dkk. 2012. Model Epidemi SEIR Pada Penyebaran Penyakit Campak dengan Pengaruh Vaksinasi. Unnes Journal of Mathematics, Vol. 1, No 2, hal. 110-117.

Maesaroh U., Sugiyanto. 2013. Model Matematika Untuk Kontrol Campak Menggunakan Vaksinasi. Fourier, Vol.2 thn 2013, hal. 97-110. Fakultas Sains dan Teknologi, Universitas Islam Negeri Sunan Kalijaga, Yogyakarta.

Suandi Dhani. 2018. Analisis Dinamik pada Model Penyebaran Penyakit Campak dengan Pengaruh Vaksin Permanen. Jurnal Kubik, Vol. 2, No. 2, Agt 2018, hal. 1-10.

Tu, P.N.V., 1994. Dinamycal System an Introduction with Applications in Economics and Biology. Second Revision and Enlarged Edition. Springer-Verlag., New York.

Downloads

Published

2019-06-27

Issue

Section

Research Articles

Deprecated: json_decode(): Passing null to parameter #1 ($json) of type string is deprecated in /home/journal33/public_html/plugins/generic/citations/CitationsPlugin.inc.php on line 49