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All Journal Indonesian Journal of Education and Mathematical Science Jurnal Ilmu Komputer dan Matematika
Nur Alisa
Universitas Muhammadiyah Kudus
Computer Science & IT Control & Systems Engineering Education Languange, Linguistic, Communication & Media Library & Information Science Mathematics

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DINAMIKA PERKEMBANGAN HIV/AIDS DI KABUPATEN KUDUS MENGGUNAKAN MODEL PERSAMAAN DIFERENSIAL NONLINEAR SIR (SUSCEPTIBLE, INFECTIOUS AND RECOVERED) Ivanna Isty Nursani; Nur Alisa; Irma Latifah; Melvin Dewi Rosita
JURNAL ILMU KOMPUTER DAN MATEMATIKA Vol 4, No 2 (2023): JURNAL ILMU KOMPUTER DAN MATEMATIKA
Publisher : Universitas Muhammadiyah Kudus

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26751/jikoma.v4i2.1982

Abstract

HIV/AIDS is the Human Immunodeficiency Virus, or HIV is often abbreviated as a deadly virus from two lentivirus species that cause it. The virus attacks humans and attacks the immune system, so that the body becomes weak in fighting infection. HIV/AIDS will also occur in Kudus Regency in 2021, there will be an additional 124 cases of HIV/AIDS sufferers in Kudus. But for this year, from January to October 2022, the number of confirmed cases has grown by 184. Head of Disease Prevention and Control, Kudus District Health Office (DKK), Darsono, said the phenomenon of the rise of 'open BO' was one of the factors for the rapid growth of HIV/AIDS cases. Therefore, a study was conducted to determine the dynamics of HIV/AIDS development in Kudus District using the SIR nonlinear differential equation model. The data used is data on the number of people living with HIV/AIDS and the total population in Kudus Regency for 2020 – 2021 from the Central Statistics Agency and the Kudus District Health Office. In this study, it was concluded that there would be an epidemic of HIV/AIDS in a period of up to 50 years.
Application of Runge Kutta Fehlberg (RKF45) Method as a Numerical Analysis to SIR Model of Tuberculosis Transmission in Central Java Nur Alisa; Ade Ima Afifa Himayati; Findasari Findasari
Indonesian Journal of Education and Mathematical Science Vol 6, No 3 (2025)
Publisher : Universitas Muhammadiyah Sumatera Utara (UMSU)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30596/ijems.v6i3.26789

Abstract

This study uses a three-compartment SIR model to describe the spread of tuberculosis in Central Java. Changes in individuals who are detected, recover, die naturally, and die from tuberculosis affect disease transmission. Numerical simulations are used to validate the analytical results and identify the key parameters that contribute most to disease transmission among susceptible, infected, quarantined, and recovered individuals. The numerical method used is the Runge-Kutta-Fehlberg method. Using this method, a quantitative description of the numbers of susceptible, infected, and recovered individuals is obtained, which can assist the Central Java Health Office in efforts to prevent and control the spread of tuberculosis. The SIR model obtained from the parameter determination is then solved using the Runge-Kutta-Fehlberg method. The results obtained using data from 2021–2023 show initial values of 111,120,397 for Susceptible, 157,024 for Infected, and 38,452 for Recovered, with a birth rate parameter of 0.013043, a natural mortality rate of 0.001287, a tuberculosis mortality rate of 0.041376, a transmission rate from Susceptible to Infected of 0.001411, and a recovery rate from Infected to Recovered of 0.24488 individuals. In the 50th year, there are 35,073,325 Susceptible individuals, the number of Infected individuals is 0.04, and the number of Recovered individuals is 74,774. The number of tuberculosis infection cases decreases from year to year.
Co-Authors Ade Ima Afifa Himayati Findasari Findasari Irma Latifah Ivanna Isty Nursani Melvin Dewi Rosita