Zarin Rahat, Zeb Aurang, Alshammari Fehaid Salem, Khan Amir, Khalifa Hamiden Abd El-Wahed
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 10140, Bangkok, Thailand.
Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhwa, Pakistan.
Sci Rep. 2025 Jun 2;15(1):19301. doi: 10.1038/s41598-025-04227-6.
This study proposes a novel sex-structured syphilis transmission model that incorporates key biological features such as congenital infection and disability due to long-term complications. While previous works have explored syphilis dynamics using fractional calculus, we extend this framework by introducing two additional compartments: congenitally infected newborns ( ) and individuals with syphilis-induced disabilities ( ), allowing for a more realistic representation of vertical transmission and chronic disease outcomes. The model is formulated using the Atangana-Baleanu-Caputo (ABC) fractional derivative to capture memory effects and non-local dynamics often observed in infectious disease spread. We rigorously analyze the positivity and boundedness of solutions, and establish the existence and uniqueness using Lipschitz continuity and Banach space theory. The basic reproduction number is derived to characterize disease dynamics, and both local and global stability of the disease-free equilibrium are proven. A detailed sensitivity analysis identifies the most influential parameters affecting , such as transmission probabilities, treatment rates, and the vertical transmission factor. Numerical simulations based on the Adams-Bashforth and Newton polynomial schemes validate the theoretical findings and provide insights into the potential effectiveness of various intervention strategies. Overall, this work contributes an enhanced modeling framework that integrates mathematical rigor with public health relevance, offering valuable guidance for targeted strategies to control syphilis and reduce its congenital and long-term burden.
本研究提出了一种新颖的按性别分层的梅毒传播模型，该模型纳入了诸如先天性感染和长期并发症导致的残疾等关键生物学特征。虽然先前的研究使用分数阶微积分探索了梅毒动态，但我们通过引入另外两个隔间来扩展这一框架：先天性感染新生儿（ ）和患有梅毒引起的残疾的个体（ ），从而更真实地呈现垂直传播和慢性病结果。该模型使用阿坦加纳 - 巴莱亚努 - 卡普托（ABC）分数阶导数来制定，以捕捉传染病传播中经常观察到的记忆效应和非局部动态。我们严格分析了解的正性和有界性，并利用利普希茨连续性和巴拿赫空间理论建立了存在性和唯一性。推导了基本再生数 以表征疾病动态，并证明了无病平衡点的局部和全局稳定性。详细的敏感性分析确定了影响 的最具影响力的参数，如传播概率、治疗率和垂直传播因子。基于亚当斯 - 巴什福思和牛顿多项式方案的数值模拟验证了理论结果，并深入了解了各种干预策略的潜在有效性。总体而言，这项工作贡献了一个增强的建模框架，该框架将数学严谨性与公共卫生相关性相结合，为控制梅毒并减轻其先天性和长期负担的针对性策略提供了有价值的指导。
