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All Journal Square : Journal of Mathematics and Mathematics Education Jurnal Teknik Sipil Macca
Hajar, Muhammad Ibnu
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Civil Engineering, Building, Construction & Architecture Education Engineering Mathematics

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Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue Diana, Arista Fitri; Hajar, Muhammad Ibnu; Ikhtiyar, Zakaria Bani; Aulia, Lathifatul
Square : Journal of Mathematics and Mathematics Education Vol 6, No 1 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.1.21018

Abstract

Dengue fever transmission in Indonesia has an advanced amount. In this article, dynamic model of interaction between human and Aedes aegypti mosquitos is learned. The SEIRRD (Susceptible, Exposed, Infected, Recovered, Deceased) model is used in this article. The prurpose in this model is to describe the stability of dengue transmission, so that we can analyze the developed of epidemic model in mathemtic field. Using NGM method to analyze basic reproduction number and applying Routh-Hurwitz criteria method to show the local stability of model. Then, two equilibrium points, called endemic and non-endemic equilibrium points, are obtained. The result of basic reproduction number is described the stability analysis. If basic reproduction number less then one, the endemic equilibrium point is locally asymptotically stable and otherwise. Local stability analysis at the equilibrium point is determined through parameter analysis. Furthermore, numerical simulations are carried out by fitting the data to obtaine the result of the parameters. The results of numerical simulations explaine the spread of dengue transmission Keywords: Dynamic Model, Epidemic Model, Equilibrium Point, Local Stability, Routh Hurwitz
Kajian Tingkat Pelayanan dan Efektivitas Fasilitas Jembatan Penyeberangan Orang pada Ruas Jalan Perintis Kemerdekaan R, Muhammad Reza Aizar; Hajar, Muhammad Ibnu; Said, Lambang Basri; Massara, Asma; Watono
Jurnal Teknik Sipil MACCA Vol. 7 No. 1 (2022): Jurnal Teknik Sipil MACCA
Publisher : Universitas Muslim Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33096/wxsrea03

Abstract

Jembatan penyeberangan orang adalah fasilitas bagi pejalan kaki yang digunakan untuk menyeberangi jalan yang padat lalu lintas menggunakan jembatan. Tujuan dari penelitian ini ialah untuk mengetahui tingkat pelayanan dan nilai efektivitas jembatan penyeberangan orang (JPO) di depan Makassar Town Square pada ruas jalan Perintis Kemerdekaan. Analisis dilakukan dengan cara menghitung volume pejalan kaki yang melalui dan yang tidak melalui jembatan penyeberangan orang (JPO) di jam sibuk pagi, siang dan sore. Berdasarkan hasil analisis data Arus (flow) didapatkan hasil sebesar Q = 0,255 pejalan kaki/m/menit, untuk analisis data keceptan rata – rata ruang (space mean speed) didapatkan hasil sebesar (Vs) = 1,200 m/menit, kecepatan rata – rata waktu (time mean speed) didapatkan hasil sebesar (Vt) = 1,204 m/menit, untuk analisis data kepadatan (density) didapatkan hasil sebesar D = 0,212 pejalan kaki/m2, dan untuk analisis data ruang (space) didapatkan hasil sebesar S = 4,712 m2/pejalan kaki. Sehingga, tingkat pelayanan jembatan penyeberangan orang di depan Makassar Town Square pada ruas jalan Perintis Kemerdekaan berada pada pada kategori LOS B. Sedangkan untuk hasil analisis data efektivitas jembatan penyeberangan orang (JPO) didapatkan hasil sebesar 43,496%, sehingga tingkat efektivitas jembatan penyeberangan orang (JPO) di depan Makassar Town Square pada ruas jalan Perintis Kemerdekaan berada pada kategori “Cukup Efektif”.
Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue Diana, Arista Fitri; Hajar, Muhammad Ibnu; Ikhtiyar, Zakaria Bani; Aulia, Lathifatul
Square : Journal of Mathematics and Mathematics Education Vol. 6 No. 1 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.1.21018

Abstract

Dengue fever transmission in Indonesia has an advanced amount. In this article, dynamic model of interaction between human and Aedes aegypti mosquitos is learned. The SEIRRD (Susceptible, Exposed, Infected, Recovered, Deceased) model is used in this article. The prurpose in this model is to describe the stability of dengue transmission, so that we can analyze the developed of epidemic model in mathemtic field. Using NGM method to analyze basic reproduction number and applying Routh-Hurwitz criteria method to show the local stability of model. Then, two equilibrium points, called endemic and non-endemic equilibrium points, are obtained. The result of basic reproduction number is described the stability analysis. If basic reproduction number less then one, the endemic equilibrium point is locally asymptotically stable and otherwise. Local stability analysis at the equilibrium point is determined through parameter analysis. Furthermore, numerical simulations are carried out by fitting the data to obtaine the result of the parameters. The results of numerical simulations explaine the spread of dengue transmission Keywords: Dynamic Model, Epidemic Model, Equilibrium Point, Local Stability, Routh Hurwitz
Co-Authors Aulia, Lathifatul Diana, Arista Fitri Ikhtiyar, Zakaria Bani Lambang Basri Said Massara, Asma R, Muhammad Reza Aizar Watono