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Title: | Analisis Kestabilan Model Penyebaran Penyakit Demam Berdarah dengan Penularan Vertikal pada Vektor |
Other Titles: | Stability Analysis of the Dengue Disease Spread Model with Vertical Transmission of Vectors |
Authors: | Sianturi, Paian Kusnanto, Ali Hafizha, Tazkia Nuur |
Issue Date: | 2024 |
Publisher: | IPB University |
Abstract: | Demam berdarah merupakan penyakit yang disebabkan oleh virus dengue yang ditularkan melalui gigitan nyamuk betina Aedes aegypti. Nyamuk betina yang terinfeksi dapat menularkan virus kepada telurnya. Pada penelitian ini dianalisis kestabilan model demam berdarah dengan penularan vertikal pada vektor. Tujuan penelitian ini adalah untuk menganalisis pengaruh beberapa parameter pada dinamika populasi. Bilangan reproduksi dasar ditentukan dengan menggunakan the next generation matrix. Diperoleh dua titik tetap, yaitu titik tetap bebas penyakit dan titik tetap endemik. Berdasarkan hasil analisis kestabilan titik tetap menggunakan kriteria Routh-Hurwitz, diperoleh bahwa jika R0 > 1 maka titik tetap bebas penyakit tak stabil dan titik tetap endemik stabil. Penurunan laju kontak efektif vektor ke manusia dan peningkatan laju kematian alami nyamuk menyebabkan penyakit demam berdarah tidak akan menyebar dalam populasi. Dengue fever is a disease caused by the dengue virus that is transmitted through the bite of female Aedes aegypti. Infected female mosquitoes can transmit the virus to their eggs. This study analyzed the stability of the dengue fever model with vertical transmission in vectors. The purpose of this study is to analyze the effect of several parameters on population dynamics. The basic reproduction number was determined by using the next generation matrix. Two equilibrium points were obtained i.e., disease-free equilibrium point and endemic equilibrium point. Based on the analysis of the stability of the equilibrium points using the Routh-Hurwitz criterion, it was found that if R0 > 1 then the disease-free equilibrium point would be unstable, while the endemic equilibrium point was stable. The decrease in the effective contact rate of vectors to humans and the increase in the natural mortality rate of mosquitoes cause dengue fever to not spread in the population. |
URI: | http://repository.ipb.ac.id/handle/123456789/157862 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
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cover_G5401201007_bb034ab8912645f098f32e1349c02940.pdf | Cover | 880.01 kB | Adobe PDF | View/Open |
fulltext_G5401201007_4ea1ab3c740b42898d4a2d4d9996f59d.pdf Restricted Access | Fulltext | 3.49 MB | Adobe PDF | View/Open |
lampiran_G5401201007_f5e1edb8e8e0481db6ff99af88a134c1.pdf Restricted Access | Lampiran | 1.62 MB | Adobe PDF | View/Open |
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