ANALISIS DINAMIK DAN KONTROL OPTIMAL MODEL PENYEBARAN HOAKS PADA MEDIA SOSIAL

TIANA FITRI, . (2023) ANALISIS DINAMIK DAN KONTROL OPTIMAL MODEL PENYEBARAN HOAKS PADA MEDIA SOSIAL. Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

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Abstract

Penelitian ini membahas model penyebaran hoaks pada media sosial dengan kontrol optimal berupa penindakan hukum terhadap penyebar hoaks. Pada model tersebut dilakukan analisis dinamik meliputi penentuan titik kesetimbangan, angka reproduksi dasar, dan analisis kestabilan titik kesetimbangan. Hasil analisis dinamik dan simulasi numerik menunjukkan bahwa model memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas hoaks (E1) dan titik kesetimbangan endemik (E2). Kestabilan titik kesetimbangan bebas hoaks dan titik ketimbangan endemik bergantung pada R0. Jika R0 < 1, maka titik kesetimbangan bebas hoaks stabil asimtotik dan jika R0 > 1, maka titik kesetimbangan endemik stabil asimtotik dengan syarat memenuhi kriteria Routh-Hurwitz. Selanjutnya, model diberikan kontrol penindakan hukum terhadap penyebar hoaks dengan menggunakan Prinsip Minimum Pontryagin dan penyelesaian numeriknya menggunakan metode Sweep Maju-Mundur untuk menunjukkan pengaruh dari pemberian kontrol. ***** This research discusses a model of the spread of hoaxes on social media with optimal control in the form of legal action against hoax spreaders. The dynamic analysis of the model includes the determination of the equilibrium point, the basic reproduction number, and the stability analysis of the equilibrium point. The results of dynamic analysis and numerical simulation show that the model has two equilibrium points, namely the hoax-free equilibrium point (E1) and the endemic equilibrium point (E2). The stability of the hoax-free equilibrium point and the endemic equilibrium point depends on R0. If R0 < 1, then the hoax-free equilibrium point is asymptotically stable and if R0 > 1, then the endemic equilibrium point is asymptotically stable provided that it satisfies the Routh-Hurwitz criterion. Furthermore, the model is given a law enforcement control against hoax spreaders using Pontryagin’s Minimum Principle and its numerical solution using the Sweep method Forward-Backward method to show the effect of the control.

Item Type:	Thesis (Sarjana)
Additional Information:	1). Dr. Eti Dwi Wiraningsih, S.Pd., M.Si. ; 2). Dr. Lukita Ambarwati, S.Pd., M.Si.
Subjects:	Sains > Matematika
Divisions:	FMIPA > S1 Matematika
Depositing User:	Users 18948 not found.
Date Deposited:	04 Sep 2023 06:25
Last Modified:	04 Sep 2023 06:25
URI:	http://repository.unj.ac.id/id/eprint/40493

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