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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Jambura Journal of Biomathematics (JJBM)
Akanni, John Olajide
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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A Non-linear Fractional Model for Analyzing the Impact of Vaccination on the Dynamics of COVID-19 in Indonesia Akanni, John Olajide; Abidemi, Afeez; Fatmawati, Fatmawati; Chukwu, Chidozie Williams
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30383

Abstract

COVID-19, yang disebabkan oleh virus corona baru SARS-CoV-2, masih menjadi tantangan kesehatan masyarakat global. Studi ini mengusulkan dan menganalisis model matematika untuk memantau perkembangan COVID-19 dan menilai dampak upaya imunisasi. Model tersebut menggabungkan faktor-faktor epidemiologi utama dan dikalibrasi menggunakan data yang tersedia untuk umum tentang kasus harian kumulatif COVID-19 di Indonesia, yang berlangsung dari 1 Juli 2021 hingga 21 Juli 2022. Angka reproduksi dasar, , diturunkan dan keadaan ekuilibrium ditetapkan. Analisis bifurkasi dilakukan menggunakan Teorema Manifold Pusat untuk memahami potensi dinamika transisi penyakit. Analisis sensitivitas lokal mengungkapkan bahwa tingkat penularan efektif (), tingkat kematian alami (), tingkat vaksinasi () dan tingkat pengobatan untuk individu bergejala () adalah parameter yang paling berpengaruh. Simulasi model menunjukkan bahwa mengurangi penularan, meningkatkan pengobatan, dan meningkatkan penyerapan vaksin secara signifikan mengurangi beban penyakit. Untuk lebih menangkap efek memori yang melekat dalam penularan penyakit, model diperluas ke kerangka turunan Caputo orde fraksional. Keberadaan, keunikan, dan stabilitas model fraksional ditetapkan melalui teori titik tetap. Hasil numerik menunjukkan bahwa penurunan dalam orde fraksional sedikit menggeser dinamika, yang menunjukkan perubahan perilaku dalam menanggapi wabah sebelumnya. Temuan ini memberikan informasi berharga tentang strategi pengendalian penyakit dan menyoroti pentingnya langkah-langkah kesehatan masyarakat yang berkelanjutan.
MATHEMATICAL MODEL OF DENGUE HEMORRHAGIC FEVER SPREAD WITH DIFFERENT LEVELS OF TRANSMISSION RISK Herdicho, Faishal Farrel; Hakim, Nabil Azizul; Fatmawati, Fatmawati; Alfiniyah, Cicik; Akanni, John Olajide
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1649-1666

Abstract

Dengue Haemorrhagic Fever (DHF) is a vector-borne disease caused by the dengue virus, transmitted to humans through the bite of an infected female Aedes aegypti mosquito. DHF is prevalent in tropical regions, necessitating mathematical modeling to better understand its dynamics and predict its spread. This study develops and analyzes a mathematical model for DHF transmission that incorporates seven compartments to reflect different transmission risk levels. Stability analysis of the disease-free and endemic equilibria was conducted, with the basic reproduction number used to classify the conditions under which DHF transmission is controlled or endemic . Key model parameters were estimated using DHF case data from East Java in 2018, employing a genetic algorithm (GA) to optimize the estimation process. The GA approach achieved a mean absolute percentage error (MAPE) of , ensuring high accuracy in parameter values. Furthermore, the basic reproduction number was determined to be , which is greater than one, confirming that DHF remains endemic in East Java. Sensitivity analysis identified the mosquito biting rate , mosquito mortality rate , and transmission rates as the most critical factors influencing . Numerical simulations demonstrated the effects of these key parameters on both and the symptomatic human population . An increase in , , or significantly amplified and , while a rise in had the opposite effect, reducing both transmission and infections. These results underscore the critical role of vector control strategies, such as increasing mosquito mortality and reducing breeding sites, in mitigating DHF outbreaks. This study highlights the utility of combining mathematical modeling with genetic algorithm-based parameter estimation to provide accurate insights into disease dynamics and inform effective control measures.
Co-Authors Abidemi, Afeez Alfiniyah, Cicik Chukwu, Chidozie Williams Fatmawati, Fatmawati Hakim, Nabil Azizul Herdicho, Faishal Farrel