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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

Stability Analysis and Estimation of the Basic Reproductive Ratio Using a SEITA-Type Model of HIV/AIDS Spread in Cilegon City Mahuda, Isnaini; Sholihin, Miftahus; Sonda, Atia; Sari, Putri Dina; Asshiddieqie, Rafi Ramadhan; Udiansyah, Naufal Arrafi
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.9586

Abstract

HIV/AIDS remains a critical global health issue that requires a multidisciplinary approach to reduce its transmission. Understanding the transmission dynamics through mathematical models can assist in formulating effective intervention strategies. This study aims to analyze the stability of HIV/AIDS transmission model in Cilegon City using five compartments, namely Susceptible, Educated, Infected, Treatment, and AIDS or SEITA-type model. Subsequently, the basic reproductive ratio (R0) is estimated by constructing the Next Generation Matrix (NGM) and the dynamic simulation of the model is carried out using parameters calibrated based on HIV/AIDS data from Cilegon City. The Analysis of stability equilibrium points show that the disease-free equilibrium point is locally asymptotically stable when R0<1 and when R0>1 then endemic equilibrium point is locally asymptotically stable. Furthermore, the numeric simulation results indicate that the increasing parameter transition rate from the susceptible subpopulation to the educated subpopulation, the ARV treatment rate applied to the infected subpopulation and decreasing parameter transition rate from the educated subpopulation to the susceptible subpopulation, could suppress the basic reproduction number, thereby enabling effective control of the HIV/AIDS spread in Cilegon City.
Co-Authors Abdul Kholiq Abdul Kholiq Agus Setia Budi Ahmad Fauzi Hendratmoko Alfarisi, Muhammad Nur Fikri Alisya, Regina Dwirahma AlMuhibbi, Muhammad Rayendra Anam, M. Khairul Ansori, Yulian Arief Rahman Arief Rahman Arina, Faula Arshad, Mohamad Syafwan Asmaraningtyas, Kinanthi Trah Asshiddieqie, Rafi Ramadhan Atia Sonda Aulia Ikhsan Azizah, Luluk Nur Azza Abidatin Bettaliyah AZZA ABIDATIN BETTALIYAH Bagus Nur Bakti Aji Bagus Nur Bakti Aji Cindy Suryanti Darnis, Febriyanti Delano, M. Fabian Reinhard Dinar Mahdalena Leksana 1 Erna Hayati Erna Hayati, Erna Erry Anggraini ERRY ANGGRAINI Faiz, Syukron Farizki, Achmad Nurasel FATHARANI, ATIKA Fatkhul U, M. Miftah Febriyanti Darnis Firdaus, Muhammad Alvin Fudzee, Mohd Farhan Md Gusman, Taufik Hamid, Rahayu A Ichsan, Andhika Muhamad Ismail, Mohd Norasri Izz, Aiz Ahmad Fa’iz Dliya’ul KIKI SEPTARIA Lilik Anifah M. Ghofar Rohman M. Rosidi Zamroni M. ZAKI QOMARUDDIN Mahuda, Isnaini Masruroh MASRUROH Megawati Indriani Mohd Farhan MD Fudzee, Mohd Farhan Mufrody, Moh Adam Mustain Mustain Nafiiyah, Nur Nur Nafi'iyah Nur Nafi’iyah Nurroziqin, M Chabib Nurul Aswa Omar Nurul Ftria ApriLliani Pertiwi, Dinda Dwi Anugrah Prastowo, Diko Pratiwi, Putri Septiani Indah Prisma Nanda Prsatama, Febrian Abie Rahayu A Hamid Rahma, Midia Retno Wardhani Rofika Arista Sari, Putri Dina Setia Budi, Agus Sika Azkia, Czidni Silvia Agustin Siti Mujilahwati Sulaiman, Akhmad Nurali Surojuddin, Eko Titin Nurbella Udiansyah, Naufal Arrafi Ulum, M. Miftah Fatkhul Umam, Moch. Zuhrul Vanesta Ikhsana Putri Maulana Wati, Efi Neo WICAKSONO, AGUNG SATRIO Yulian Ansori Zirby, Qonit Zumrotus Shalekhah