Analisis Kestabilan Global dengan Menggunakan Fungsi Lyapunov pada Model Dinamik Epidemik SIR dengan Efek Psikososial

Nurjanah, Lisna (2018) Analisis Kestabilan Global dengan Menggunakan Fungsi Lyapunov pada Model Dinamik Epidemik SIR dengan Efek Psikososial. Diploma thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

Skripsi ini membahas tentang analisis kestabilan global dengan menggunakan fungsi Lyapunov pada model dinamik epidemik SIR. Populasi manusia pada Skripsi ini diasumsikan menjadi tiga populasi yaitu individu rentan (susceptible), terinfeksi (infected) dan kebal (recovered). Pada titik tetap bebas penyakit dapat disimpulkan bahwa titik tetap bersifat stabil asimtot global karena definit positif dengan dan turunan fungsi tersebut semi definit negatif jika . Sedangkan pada titik tetap endemik dapat disimpulkan bahwa titik tetap bersifat stabil global karena definit positif dan turunan fungsi tersebut semi definit negatif umtuk setiap dan . This research discusses the analysis of global stability using Lyapunov function in the dynamics model of the SIR epidemic. Human population diveded into three population such as Susceptible (S), Infected (I) and Recovered (R). The author will examine the states of disease free and endemic equilibrium. The result obtained that desease free equilibrium is global asymptoticaly stable because (definite positive), (definite negative) if . The result obtained that the endemic equilibrium is globaly stable because (definite positive) if , (semi definite negative) and .

Item Type: Thesis (Diploma)
Uncontrolled Keywords: Model Epidemik SIR;Keadaan Ekuilibrium;Fungsi Lyapunov;
Subjects: Applied mathematics
Applied mathematics > Special Topics of Applied Mathematics
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Lisna Nurjanah
Date Deposited: 04 Jun 2018 08:02
Last Modified: 04 Jun 2018 08:02
URI: http://digilib.uinsgd.ac.id/id/eprint/10140

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