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Title: | Analisis Kestabilan Model Penyebaran Penyakit Leptospirosis Tipe SIRS |
Other Titles: | Stability Analysis of SIRS Model for Leptospirosis Disease Spread |
Authors: | Sianturi, Paian Kusnanto, Ali ANDRIANI, RIZKA DWI |
Issue Date: | 2024 |
Publisher: | IPB University |
Abstract: | Leptospirosis merupakan penyakit yang disebabkan oleh bakteri Leptospira
yang dapat menularkan ke manusia dan hewan. Model SIRS dalam populasi
manusia dan SI dalam populasi tikus digunakan untuk mempelajari analisis
kestabilan dan simulasi numerik dalam dinamika penyebaran penyakit
Leptospirosis. Hasil analisis diperoleh dua titik tetap, yaitu titik tetap bebas
penyakit dan titik tetap endemik. Titik tetap bebas penyakit akan stabil jika ℛ! < 1
dan titik tetap endemik akan stabil jika ℛ! > 1. Hasil numerik menunjukkan bahwa
kenaikan tingkat kematian alami tikus dan penurunan tingkat penularan dari tikus
rentan ke tikus terinfeksi akan mengakibatkan nilai ℛ! menurun. Upaya untuk
menurunkan laju penularan penyakit dapat dilakukan dengan menaikkan tingkat
kematian alami tikus dan menurunkan tingkat penularan dari tikus rentan ke tikus
terinfeksi. Leptospirosis is a disease caused by Leptospira bacteria that can transmit to humans and animals. SIRS model in human population and SI model in rat population are used to study the stability analysis and numerical simulation in the dynamics of Leptospirosis disease spread. The analysis results obtained two fixed points, which are disease-free fixed point and endemic fixed point. The disease-free fixed point will be stable if ℛ! < 1 and the endemic fixed point will be stable if ℛ! > 1. Numerical results show that an increase in the natural mortality rate of rats and a decrease in the transmission rate from susceptible rats to infected rats will result in a decrease in the ℛ! value. Measures to reduce the rate of disease transmission can be made by increasing the natural mortality rate of rats and decreasing the transmission rate from susceptible rats to infected rats. |
URI: | http://repository.ipb.ac.id/handle/123456789/157861 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
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cover_G5401201037_555815287fac4c1b91ec30369285f9ec.pdf | Cover | 1.7 MB | Adobe PDF | View/Open |
fulltext_G5401201037_78938885e16948d2bda6ed4915e3ff6c.pdf Restricted Access | Fulltext | 4.4 MB | Adobe PDF | View/Open |
lampiran_G5401201037_3f4a05faf4524da7a86ef8a3a03a7046.pdf Restricted Access | Lampiran | 2.36 MB | Adobe PDF | View/Open |
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