Mathematical Model for MERS-COV Disease Transmission with Medical Mask Usage and Vaccination
Abstract
This study developed a model of the spread of MERS-CoV disease using the SEIR model which was added by a health mask and vaccination factor as a preventive measure. The population is divided into six subpopulations namely susceptible subpopulations not using health masks and using health masks, exposed subpopulations, infected subpopulations not using health masks and using health masks, and recovering subpopulations. The results are obtained two equilibrium points, namely disease-free equilibrium points and endemic equilibrium points. Analysis of the stability of the disease-free equilibrium point using linearization around the equilibrium point. As a result, the asymptotic stable disease-free local equilibrium point if the base reproduction number is less than one. Numerical simulation models for MERS-CoV disease are carried out in line with the analysis of model behavior.
Keywords: MERS-CoV, SEIR Model, Stability Equilibrium Point, Basic Reproduction Number.
Abstrak
Penelitian ini mengembangkan model penyebaran penyakit MERS-CoV menggunakan model SEIR yang ditambahkan faktor masker kesehatan dan vaksinasi sebagai upaya pencegahan. Populasi dibagi menjadi enam subpopulasi yaitu subpopulasi rentan tidak menggunakan masker kesehatan dan menggunakan masker kesehatan, subpopulasi laten, subpopulasi terinfeksi tidak menggunakan masker kesehatan dan menggunakan masker kesehatan, serta subpopulasi sembuh. Hasilnya diperoleh dua titik ekuilibrium yaitu titik ekulibrium bebas penyakit dan endemik. Analisis kestabilan titik ekuilibrium bebas penyakit menggunakan linearisasi disekitar titik ekuilibrium. Hasilnya, titik ekuilibrium bebas penyakit stabil asimtotik lokal jika bilangan reproduksi dasar kurang dari satu. Simulasi numerik model untuk penyakit MERS-CoV yang dilakukan sejalan dengan analisis perilaku model.
Kata kunci: MERS-CoV, Model SEIR, Kestabilan Titik Ekuilibrium, Bilangan Reproduksi Dasar.
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DOI: 10.15408/inprime.v1i2.13553
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