Althubyani Mohammed, Adam Haroon D S, Alalyani Ahmad, Taha Nidal E, Taha Khdija O, Alharbi Rasmiyah A, Saber Sayed
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia.
Department of Basic Sciences, Deanship of the Preparatory Year, Najran University, Najran, Saudi Arabia.
Sci Rep. 2025 Apr 22;15(1):13921. doi: 10.1038/s41598-025-95943-6.
Zoonotic diseases, which are transmitted between animals and humans, pose significant public health challenges, especially in regions with high human-wildlife interactions. This study presents a novel fractional-order mathematical model to analyze the transmission dynamics of zoonotic diseases between baboons and humans in the Al-Baha region. The model incorporates the Atangana-Baleanu fractional derivative to account for memory effects and spatial heterogeneity, offering a more realistic representation of disease spread. The fractional Euler method is employed for numerical simulations, enabling accurate predictions of infection trends under various fractional orders. Stability analysis, conducted via the Banach fixed-point theorem and Picard iterative method, confirms the model's robustness, while Hyers-Ulam stability ensures its reliability. Additionally, control strategies, including sterilization, food access restriction, and human interaction reduction, are integrated into the model to assess their effectiveness in disease mitigation. Simulation results highlight the impact of fractional-rder dynamics on disease persistence, showing that lower fractional orders correspond to prolonged infections due to memory effects. These findings underscore the significance of fractional calculus in epidemiological modeling and provide valuable insights for designing effective zoonotic disease control strategies.
人畜共患病在动物和人类之间传播，给公共卫生带来了重大挑战，尤其是在人类与野生动物互动频繁的地区。本研究提出了一种新颖的分数阶数学模型，用于分析巴哈地区狒狒和人类之间人畜共患病的传播动态。该模型采用阿坦加纳 - 巴莱努分数阶导数来考虑记忆效应和空间异质性，能更真实地反映疾病传播情况。采用分数阶欧拉方法进行数值模拟，可在不同分数阶下准确预测感染趋势。通过巴拿赫不动点定理和皮卡迭代法进行的稳定性分析证实了模型的稳健性，而海尔 - 乌拉姆稳定性确保了其可靠性。此外，将包括绝育、限制食物获取和减少人类互动在内的控制策略纳入模型，以评估它们在减轻疾病方面的有效性。模拟结果突出了分数阶动力学对疾病持续存在的影响，表明较低的分数阶由于记忆效应会导致感染持续时间延长。这些发现强调了分数阶微积分在流行病学建模中的重要性，并为设计有效的人畜共患病控制策略提供了有价值的见解。
