Advanced mathematical modeling of syphilis transmission dynamics and disability outcomes in sex-structured populations
摘要
This article presents a comprehensive study on the dynamics of syphilis transmission through the formulation of nonlinear fractional differential equations that incorporate crucial controls, specifically targeting the prevention, treatment, and long-term disability associated with syphilis in infected males and females. The model yields two equilibrium states: the syphilis-free equilibrium (SFE) and the syphilis-present equilibrium (SPE). To gauge the potential for disease control, the basic reproduction number is derived, serving as a key parameter for assessing transmission mitigation strategies. Subsequently, the conditions for both local and global stability of the syphilis-free equilibrium are established. The stability analysis reveals that the model is locally asymptotically stable upon satisfying the Routh–Hurwitz criteria and globally asymptotically stable. Employing the Atangana–Baleanu–Caputo (ABC) operator enhances the precision of the analysis. The fractional sex-structured syphilis model’s existence and uniqueness for solutions are established through fixed point theorems. The model’s fundamental properties are thoroughly examined, and stability analysis is conducted. To obtain numerical solutions, both the Newton polynomial and Adams–Bashforth methods are employed, providing a robust computational framework for understanding the intricate dynamics of the fractional sex-structured syphilis model. This study contributes valuable insights into the potential control measures for syphilis transmission, combining theoretical analyses with numerical simulations for a comprehensive understanding of the model’s behavior.