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PENYELESAIAN MODEL PENYEBARAN PENYAKIT ISPA DENGAN MENGGUNAKAN METODE RUNGE KUTTA FEHLBERG DI PROVINSI SULAWESI SELATAN: Completion Of The Spread Of Ari Disease Distribution Model Using The Runge Kutta Fehlberg Method In South Sulawesi Province Nurazizah, Nurazizah; Nurman, Try Azisah; Syata, Ilham
Al-Aqlu: Jurnal Matematika, Teknik dan Sains Vol. 2 No. 1 (2024): Januari 2024
Publisher : Yayasan Al-Amin Qalbu

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59896/aqlu.v2i1.55

Abstract

This stud discusses the analysis and simulation of acute respiratory infection (ISPA) in South Sulawesi Province by applying the RLTSM used the Fehlberg’s Runge-Kutta method. The research is an applied research type with the aim of obtaining a model of the spread of acute respiratory infection and knowing the numerical solution of the mpdel in predicting cases future acute respiratory infection. The mathematical model for acute respiratory infection is in the farm of a system of diffrential equations that includes the variables R (Susceptible), L (Exposed), T (Infected), S (Recovered), dan M (Death). The research results obtained in 2023 with h=0,01 years using the Fehlberg’s Runge-Kutta method with initial values of R0 =458.665, L0 = 165.670, T0 = 141.755, S0 = 103.217, M0 = 9  is R100 =681.560, L100 = 107.068, T0 = 141.755, S100 = 167.445, M100 = 25.248, for order 4 results and R100 =681.559, L100 = 107.070, T100 = 57.208, S100 = 167.442, M100 = 25.247, for order 5 results. The rate of the susceptible population has increased, the exposed and infected population has decreased, the recovered population has increased and then decreased, and the death population has increased and then stabilized
SOLUSI NUMERIK MODEL PENYAKIT ANEMIA MENGGUNAKAN METODE RUNGE KUTTA ORDE EMPAT DI KABUPATEN GOWA: Numerical Solution Of Anemia Disease Using The Runge-Kutta Fourth-Order Method Syam, Nur; Syata, Ilham; Nurman, Try Azisah
Al-Aqlu: Jurnal Matematika, Teknik dan Sains Vol. 2 No. 2 (2024): Juli 2024
Publisher : Yayasan Al-Amin Qalbu

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59896/aqlu.v2i2.103

Abstract

This study aims to solve the mathematical model of anaemia disease numerically using the Runge-Kutta fourth-order method. The mathematical model used is a SAR model in the form of a system of differential equations that includes the number of susceptible populations (S), anaemic populations (A), and recovered human populations (R) as initial values. This model is analysed and simulated with the values of µ, α, β, ε, π as parameters and carried out as many as several iterations with an interval time or h= 0.5 months. The initial values given are S0 = 12881,  A0 = 129, R0 = 129. The simulation results in the first iteration are the rate of susceptible population (S) = 12754 , anaemic population (A) = 128 and recovered population (R) = 192 . In the second iteration the rate of susceptible population (S) = 12630, anaemic population (A) = 126 and recovered population (R) = 254 . From the results obtained it can be concluded that the rate of susceptible population and anaemic population has decreased, while for the recovered population has increased.
ANALISIS KESTABILAN DAN SENSITIVITAS MODEL KECANDUAN FILM KARTUN: Stability and Sensitivity Analysis of The Cartoon Addiction Model Syata, Ilham; Halim, St. Nur Humairah
Al-Aqlu: Jurnal Matematika, Teknik dan Sains Vol. 4 No. 1 (2026): Januari 2026
Publisher : Yayasan Al-Amin Qalbu

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59896/aqlu.v4i1.503

Abstract

This study aims to develop a model of cartoon addiction and analyze the stability of fixed points and parameter sensitivity. The novelty of this study lies in the mathematical model of cartoon addiction by dividing the population into four main classes, namely vulnerable individuals, occasional viewers, addicts, and those who have permanently stopped watching cartoons. The methods used include the formulation of a mathematical model based on a system of differential equations, the calculation of the basic reproduction number using the next generation matrix approach, the analysis of fixed point stability, and the evaluation of sensitivity indices to identify parameters that affect the basic reproduction number. The results of the analysis show that the fixed point without addiction is locally asymptotically stable when , while the endemic fixed point is locally asymptotically stable when . Sensitivity analysis shows that the parameters of the entry rate of susceptible individuals () and the effective contact rate () contribute positively to the increase in , while the parameters of the transition from susceptible to not interested in cartoons (), the recovery rate from addiction (), and natural mortality () contribute to the decrease in . In conclusion, this model provides a comprehensive overview of the dynamics of cartoon addiction and can be used to design more appropriate prevention and treatment strategies in society