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All Journal Jambura Journal of Biomathematics (JJBM) Jurnal Matematika Integratif
Fatahillah, Hakan Ahmad
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Transportation

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Analisis Kemunculan Solusi Periodik dari Model Matematika Penyebaran Demam Berdarah Dengue dengan Laju Infeksi Tidak Standar Rahman, Nur Syam; Fatahillah, Hakan Ahmad; Aldila, Dipo
Jurnal Matematika Integratif Vol 21, No 1: April 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n1.60353.1-14

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).
Forward and Backward Bifurcation Analysis From an Imperfect Vaccine Efficacy Model With Saturated Treatment and Saturated Infection Fatahillah, Hakan Ahmad; Aldila, Dipo
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 2: December 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i2.28810

Abstract

This paper aims to study the saturation effect on the infection and recovery process within a Susceptible-Vaccination-Infected model featuring an imperfect vaccine efficacy. First, we nondimensionalized the model under the assumption of a constant population, resulting in the reduction of the model from three to two-dimensional differential equations. The analysis indicates the presence of a disease-free equilibrium (DFE) and potentially multiple endemic equilibria (EE) within the model. The calculation of the basic reproduction number further explains the model's solution conditions. In particular, we discovered that a backward bifurcation is possible under specific saturation effect values. Dulac's criterion confirmed the absence of a closed orbit in the solution region, suggesting the global stability of the endemic equilibrium when the basic reproduction number exceeds one. To supplement the analytical study, a numerical simulation was conducted to generate a bifurcation diagram, autonomous simulation, and global sensitivity analysis. The global sensitivity analysis revealed that changing the vaccination rate or recovery rate could significantly impact the basic reproduction number. Moreover, the bifurcation diagram depicting the relationship between the transmission rate and vaccination rate demonstrated that increasing the vaccination rate while maintaining the transmission rate can reduce the proportion of infected individuals within the population.
Co-Authors Dipo Aldila Rahman, Nur Syam