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<p>A fractional-order mathematical model for the transmission dynamics of typhoid fever incorporating treatment and reinfection effects is developed. The model is shown to be mathematically well-posed, and the stability of the endemic equilibrium is established using a Lyapunov function suitable for fractional systems. Numerical simulations are performed using the fractional Adams–Bashforth–Moulton method, and the results demonstrate that disease prevalence is increased by higher contact rates and significantly reduced by improved treatment effectiveness. It is further shown that appropriate treatment strategies can substantially lower infection levels and may drive the system toward a disease-free state. These results confirm that fractional-order modeling effectively captures memory-dependent dynamics and provides useful insight into typhoid fever control strategies.</p>

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Numerical solution of fractional order typhoid fever model via the generalized fractional Adams-Bashforth-Moulton approach

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Enejoh Jalija,
  • Jeremiah Amos,
  • William Atokolo,
  • Emmanuel Abah,
  • Agbata Benedict Celestine,
  • Godwin Onuche Acheneje,
  • Shyamsunder,
  • Bolarinwa Bolaji

摘要

A fractional-order mathematical model for the transmission dynamics of typhoid fever incorporating treatment and reinfection effects is developed. The model is shown to be mathematically well-posed, and the stability of the endemic equilibrium is established using a Lyapunov function suitable for fractional systems. Numerical simulations are performed using the fractional Adams–Bashforth–Moulton method, and the results demonstrate that disease prevalence is increased by higher contact rates and significantly reduced by improved treatment effectiveness. It is further shown that appropriate treatment strategies can substantially lower infection levels and may drive the system toward a disease-free state. These results confirm that fractional-order modeling effectively captures memory-dependent dynamics and provides useful insight into typhoid fever control strategies.