Uji Analisis Kestabilan dengan Fungsi Lyapunov pada Model Dengue Tipe DEN-1

Irina, Rachel Amadea (2023) Uji Analisis Kestabilan dengan Fungsi Lyapunov pada Model Dengue Tipe DEN-1. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penyakit Demam Berdarah Dengue adalah penyakit menular yang disebabkan oleh virus dengue dan ditularkan melalui gigitan nyamuk Aedes aegypti. Virus ini terbagi menjadi 4 Serotypes, yaitu DEN-1, DEN-2, DEN-3 dan DEN-4. Virus DEN�1 memiliki ciri khas akan menyebar dengan cepat di suatu wilayah. Namun tidak menyebabkan penyakit parah meski kasus yang ditimbulkan banyak. Terdapat dua populasi makhluk hidup yang terlibat dalam penyebaran penyakit DBD yaitu manusia sebagai host yang dimodelkan menggunakan model SEIR dan nyamuk Aedes aegypti sebagai vektor pembawa virus dengue yang dimodelkan menggunakan model SEI. Pada penelitian ini telah didapatkan 4 titik setimbang yaitu titik kesetimbangan endemik dan titik kesetimbangan bebas penyakit untuk ∧h, πv konstan pada kondisi awal t=0 dan ∧h, πv fungsi t . Berdasarkan uji analisis stabilitas dengan menggunakan fungsi Lyapunov terbukti bahwa Model Demam Berdarah Dengue stabil asimtotis global pada titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik.
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Dengue Hemorrhagic Fever Dengue is an infectious disease caused by the virus dengue and is transmitted through the bite of the mosquito Aedes aegypti. This virus is divided
into 4 Serotypes, namely DEN-1, DEN-2, DEN-3 and DEN-4. The DEN-1 virus has the characteristic of spreading quickly in an area. However, it does not cause severe disease even though there are many cases. There are two living populations involved in the spread of DHF, namely humans as host which are modeled using the SEIR model and Aedes aegypti mosquitoes as vector dengue virus carriers were modeled using the SEI model. In this study, 4 equilibrium points were obtained, namely the endemic equilibrium point and the disease-free equilibrium point for ∧h, πv are constant at the initial condition t=0 and ∧h, πv are a function of t. Based on Stability analysis test using the function Lyapunov proves that the Dengue Dengue Model Dengue is globally asymptotically stable at the disease-free equilibrium point and the endemic equilibrium point.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	dengue model, stability analysis, lyapunov function,model demam berdarah dengue, analisis stabilitas, fungsi lyapunov
Subjects:	Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Rachel Amadea Irina
Date Deposited:	03 Aug 2023 13:10
Last Modified:	03 Aug 2023 13:10
URI:	http://repository.its.ac.id/id/eprint/100743

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