Analisis Bifurkasi pada Pemodelan SEIR Penyebaran Penyakit Pneumonia dengan Pengaruh Vaksinasi di Jawa Timur

Rinawati, Sefiyah (2024) Analisis Bifurkasi pada Pemodelan SEIR Penyebaran Penyakit Pneumonia dengan Pengaruh Vaksinasi di Jawa Timur. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pneumonia adalah kondisi infeksi atau peradangan akut di jaringan paru yang disebabkan oleh berbagai mikroorganisme, seperti bakteri, virus, parasit, atau jamur.
Untuk memahami penyebaran penyakit pneumonia, penelitian ini menggunakan model
matematika SEIR, dengan penekanan khusus pada balita dengan tipe SEIR Susceptible�Exposed-Infected-Recovered. Banyaknya penderita pneumonia pada balita di Jawa Timur
sehingga diperlukan kajian tentang pemodelan SEIR yang kemudian akan di simulasi
menggunakan Runge-Kutta. Dari hasil penelitian yang telah dilakukan mengenai model
matematika SEIR didapat dua titik kesetimbangan, yaitu titik kesetimbangan non
endemik atau biasa disebut bebas penyakit dan titik kesetimbangan endemik. Hasil
dari analisis bifurkasi yang dilakukan adalah didapat nilai R0 > 1 yang memiliki arti
bahwa penyakit akan semakin menyebar luas dan berpotensi menjadi endemik. Simulasi
numerik dengan Runge-Kutta menghasilkan bahwa penerapan vaksinasi membantu
meningkatkan laju populasi sembuh.
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Pneumonia is an acute infection or inflammation of the lung tissue caused by various
microorganisms, such as bacteria, viruses, parasites, or fungi. To understand the spread
of pneumonia, this study employs the SEIR mathematical model, with a specific focus
on children under five using the SEIR type Susceptible-Exposed-Infected-Recovered. The
high incidence of pneumonia in children under five in East Java necessitates a study on
SEIR modeling, which will subsequently be simulated using the Runge-Kutta method.
The findings from the research on the SEIR mathematical model indicate two equilibrium
points: the non-endemic equilibrium point, also known as the disease-free point, and the
endemic equilibrium point. The results of the bifurcation analysis show that the basic
reproduction number R0 > 1, suggesting that the disease will continue to spread and has
the potential to become endemic. Numerical simulations using the Runge-Kutta method
demonstrate that the implementation of vaccination contributes to an increased recovery
rate within the population.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	SEIR Model, Pneumonia, Biffurcation, Runge-Kutta, Model SEIR, Pneumonia, Bifurkasi, Runge-Kutta
Subjects:	Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. Q Science > QA Mathematics > QA380 Bifurcation theory Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Sefiyah Rinawati
Date Deposited:	06 Aug 2024 04:21
Last Modified:	06 Aug 2024 04:21
URI:	http://repository.its.ac.id/id/eprint/113814

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