Analisis Kestabilan dan Bifurkasi pada Model SIS-SI Penyebaran Malaria

Mustika, Windi Ayu (2024) Analisis Kestabilan dan Bifurkasi pada Model SIS-SI Penyebaran Malaria. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Malaria masih menjadi masalah kesehatan di Indonesia, terutama di wilayah Indonesia Timur. Laporan World Malaria 2020 menyatakan bahwa Indonesia memiliki tingkat kasus malaria tertinggi kedua di Asia Tenggara. Meskipun kasus malaria di Indonesia menunjukkan tren penurunan hingga tahun 2015, namun terjadi peningkatan sejak tahun 2016. Pada tahun 2022, kasus malaria di Indonesia meningkat hingga 45,61% dibandingkan tahun sebelumnya dengan total 443.550 kasus, di mana 89% kasusnya berasal dari Provinsi Papua. Dalam Tugas Akhir ini, model SIS (Susceptible-Infected-Susceptible) digunakan untuk menggambarkan penyebaran malaria pada populasi manusia, dan model SI (Susceptible-Infected) untuk populasi nyamuk. Dengan model tersebut, dilakukan analisis yang mencakup penelitian titik ekuilibrium non endemik dan endemik, mengevaluasi stabilitas titik ekuilibrium, menghitung bilangan reproduksi dasar, serta melakukan analisis bifurkasi. Solusi numerik diperoleh dengan metode Runge-Kutta orde empat. Hasil analisis menunjukkan bahwa terdapat titik ekuilibrium non endemik dan titik ekuilibrium enedmik. Analisis bifurkasi menunjukkan adanya fenomena bifurkasi mundur pada model dengan titik kritis R0 adalah 0,00211706. Sementara itu, simulasi dengan menggunakan metode Runge-Kutta orde empat menunjukkan grafik kesetimbangan bebas penyakit yang stabil asimtotik lokal dengan nilai R0=0.0017787.
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Malaria remains a health issue in Indonesia, especially in Eastern Indonesia. The World Malaria Report 2020 states that Indonesia has the second-highest malaria case rate in Southeast Asia. Although malaria cases in Indonesia showed a declining trend until 2015, there has been an increase since 2016. In 2022, malaria cases in Indonesia increased by 45.6% compared to the previous year, totaling 443,550 cases, with 89% of the cases originating from Papua Province. In this final project, the SIS (Susceptible-Infected-Susceptible) model is used to describe the spread of malaria in the human population, and the SI (Susceptible-Infected) model for the mosquito population. Using these models, the analysis includes investigating non-endemic and endemic equilibrium points, evaluating the stability of the equilibrium points, calculating the basic reproduction number, and performing bifurcation analysis. Numerical solutions are obtained using the fourth-order Runge-Kutta method. The results of the analysis indicate the presence of a non-endemic equilibrium point and an endemic equilibrium point. The bifurcation analysis reveals the presence of a backward bifurcation phenomenon in the model with the critical point R0 is 0,00211706. Meanwhile, simulations using the fourth-order Runge-Kutta method show a disease-free equilibrium graph that is locally asymptotically stable with a value of R0=0.0017787.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	malaria, SIS-SI model, stability, bifurcation, malaria, model SIS-SI, stabilitas, bifurkasi
Subjects:	Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA380 Bifurcation theory Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Windi Ayu Mustika
Date Deposited:	08 Aug 2024 07:18
Last Modified:	08 Aug 2024 07:18
URI:	http://repository.its.ac.id/id/eprint/114151

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