Eksistensi Bifurkasi Mundur Pada Model Penyebaran Penyakit Menular Dengan Vaksinasi

Lestari, Intan Putri (2012) Eksistensi Bifurkasi Mundur Pada Model Penyebaran Penyakit Menular Dengan Vaksinasi. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Epidemik adalah kejadian berjangkitnya suatu penyakit menular dalam masyarakat yang dapat menimbulkan banyak kerugian. Untuk itu diperlukan upaya untuk menanggulangi wabah tersebut, diantaranya dengan cara tindakan pemberian vaksinasi yang bertujuan untuk memberikan pertolongan medis berupa pencegahan agar penderita tidak menjadi sumber penularan. Oleh karena itu model epidemik dikembangkan dengan menambah kompartemen vaksinasi. Dalam tugas akhir ini, dianalisa terjadinya bifurkasi mundur dari model epidemik SIS dengan vaksinasi. Eksistensi bifurkasi mundur dinalisa tanpa menggunakan normal form, tetapi cukup memperhatikan perubahan arah pada kurva titik setimbang endemik. Dari hasil analisis didapat bilangan reproduksi dasar yang menyatakan rata-rata terjadinya penularan penyakit. eksistensi bifurkasi mundur pada model epidemik SIS dengan vaksinasi dikarenakan ketidakefektifan vaksin sehingga terdapat titik kesetimbangan endemik saat bilangan reproduksi dasar kurang dari 1. Hal ini mengakibatkan pengendalian penyakit menjadi lebih sulit
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An epidemic is the outbreak of an infectious disease in a community that can cause significant harm. Therefore, efforts are needed to overcome the outbreak, including vaccination, which aims to provide medical assistance in the form of prevention so that sufferers do not become sources of infection. Therefore, the epidemic model was developed by adding a vaccination compartment. In this final project, the occurrence of backward bifurcation in the SIS epidemic model with vaccination is analyzed. The existence of backward bifurcation is analyzed without using normal form, but simply by paying attention to the change in direction of the endemic equilibrium point curve. From the analysis results, the basic reproduction number is obtained, which indicates the average occurrence of disease transmission. The existence of backward bifurcation in the SIS epidemic model with vaccination is due to the ineffectiveness of the vaccine, resulting in an endemic equilibrium point when the basic reproduction number is less than 1. This makes disease control more difficult

Item Type:	Thesis (Other)
Additional Information:	RSMa 515.392 Les e-1 2012 (weding)
Uncontrolled Keywords:	Bifurkasi Mundur, Bilangan Reproduksi Dasar, Model SIS, Vaksinasi; SIS Model, Vaccination, Stability Analysis, Basic Rproduction Number, Backward Bifurcation
Subjects:	Q Science > QA Mathematics > QA380 Bifurcation theory
Divisions:	Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	EKO BUDI RAHARJO
Date Deposited:	16 Sep 2025 07:06
Last Modified:	16 Sep 2025 07:06
URI:	http://repository.its.ac.id/id/eprint/128264

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