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Mahuda, Isnaini
Universitas Bina Bangsa
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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

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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 04, Meida Fitriani Agusutrisno Agusutrisno, Agusutrisno Ahmad Jamiluddin Fikri Ahmad Mukhlis, Ahmad Ajeng Afifah Muhartini Ajeng Afifah Muhartini Akbar Nugraha Alisya, Regina Dwirahma Anggita Megasari Anton Nasrullah, Anton Arief Rahman Arina, Faula Arta Rusidarma Putra Asep Rahmatullah Asmaraningtyas, Kinanthi Trah Asnawi Asnawi Asshiddieqie, Rafi Ramadhan Atia Sonda Ayang Fristia Maulana Beni Junedi Beni Junedi Bhat , Ishfaq Ahmad Caesarani, Sarah Dedy Khaerudin Delano, M. Fabian Reinhard Desiyani, Risma Eka Dewi Anita Layli Ernawati Ernawati Faiz, Syukron Faqihuddin Faqihuddin Febrianti, Tanti HAMIDAH Harsono, Pram Hidayanti, Nur Hidayat, Amat Himmatul Mursyidah Holilah Ichsan, Andhika Muhamad Jaka Wijaya Kusuma Junedi, Beni Kusuma, Aria Cendana M. Adlan Abizar Meilisa, Ranny Melani Dwi Agustini Miftahul Huda Miftahus Sholihin Mira Marlina Mochamad Novel Muhartini, Ajeng Afifah Nenden Gustika Maulani Nirmalasari, Dinar Nisa’, Khoirotun Nur Aini F Nurhasan Nugroho Nurhayati Oman Sahroni Oman Sharoni Pardomuan Robinson Sihombing Pertiwi, Dinda Dwi Anugrah Purwaningsih, Zenny Puspita Maelani Rahma, Midia Rahmawati, Septi Dwi Ratnasari, Silvia Regita Alfianti Rofiroh Rofiroh Rofiroh, Rofiroh Saeful Hidayat Sari, Putri Dina Septi Dwi Rahmawati SIREGAR, DINA KHAIRUNA Siti Ayu Amalia Solihin Sri Sukmawati Sri Sukmawati Suhamah, Amah Suseno, Bambang Dwi Syarif Abdullah Tanti Febrianti Taufan Talib Tubagus Bakhrul Alam Udiansyah, Naufal Arrafi Ujang Hibar Ulfi Jefri Wahyu Wiguna WICAKSONO, AGUNG SATRIO