Numerical Simulation of a Fractional SEIHRD Epidemic Model Using Adams-Bashforth-Moulton Method

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DOI: https://doi.org/10.28924/2291-8639-24-2026-47
Published: Feb 19, 2026
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Abeer Al-Nana, Iqbal M. Batiha, Ahmed Bouchenak, Shaimaa A. A. Ahmed, Numerical Simulation of a Fractional SEIHRD Epidemic Model Using Adams-Bashforth-Moulton Method, Int. J. Anal. Appl., 24 (2026), 47.

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Abeer Al-Nana, Iqbal M. Batiha, Ahmed Bouchenak, Shaimaa A. A. Ahmed

Abstract

Epidemics are infectious diseases that spread rapidly and affect large portions of the population within a specific region and timeframe. Throughout history, such outbreaks have caused devastating impacts on humanity from the Black Death, which eliminated one-third of Europe’s population during the Middle Ages, to the Spanish flu, which claimed millions of lives in the early 20th century. While treatment and prevention strategies vary depending on the nature of the disease, common measures often include quarantine, isolation, improved hygiene, and the development of vaccines and medications. In this study, we propose a hypothetical fractional-order epidemic model to investigate the potential spread of the Ebola virus during the Ramadan season of 2025. The model specifically considers the influx of pilgrims into the Kingdom of Saudi Arabia, one of the world’s leading destinations for religious tourism during Ramadan. We numerically solve the model using the Adams–Bashforth–Moulton Predictor–Corrector Method, and conduct a detailed analysis of the simulation results to better understand the dynamics of the outbreak and propose effective mitigation strategies.

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