Analisis Kemunculan Solusi Periodik dari Model Matematika Penyebaran Demam Berdarah Dengue dengan Laju Infeksi Tidak Standar

Nur Syam Rahman, Hakan Ahmad Fatahillah, Dipo Aldila

Abstract


Analisis kemunculan solusi periodik dari model penyebaran demam berdarah dengue(DBD) dibahas pada artikel ini. Model penyebaran DBD yang dibahas dibentuk menggunakan pendekatan sistem persamaan differensial berdimensi lima, yang dengan pendekatan Quassi Steady State Approximation dan asumsi populasi konstan, dapat disederhanakan menjadi sistem persamaan differensial biasa non linear berdimensi dua. Fitur menarik dari model yang dibahas terletak pada fungsi infeksi yang tidak standar untuk menggambarkan fenomena ketidakpedulian masyarakat terhadap penyebaran penyakit DBD. Analisis kemunculan bifurkasi Hopf yang berakibat pada kemunculan solusi periodik dibahas pada artikel ini secara analitik dan numerik. Simulasi numerik untuk beberapa skenario berbeda menunjukkan bahwa model yang dibahas dapat memunculkan fenomena menarik berupa bifurkasi maju, bifurkasi mundur, bifurkasi Hopf, hingga kemunculan fenomena gelembung endemik (endemic bubble).


Keywords


Model demam berdarah dengue, Bifurkasi Hopf, Solusi periodik, Sistem dinamik

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DOI: https://doi.org/10.24198/jmi.v21.n1.60353.1-14

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