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This work deals with the mathematical modelling of Typhoid fever disease dynamics using Caputo type fractional derivative. After the formulation of the model, we compute the basic reproduction number \(R_0\) and prove the local and global stability of the Typhoid-free equilibrium whenever \(R_0<1\) . For \(R_0>1\) , we prove that there exists only one endemic equilibrium which is globally asymptotically stable. Then, we prove existence and uniqueness of solution as well as its global stability using the Ulam-Hyers criterion. We finally perform numerical simulation to validate our theoretical results.

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Fractional-Order Dynamics of a Typhoid Epidemic Model

  • 会议论文

  • 发表日期：

    2025年

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  • Rubin Fandio,
  • Hamadjam Abboubakar,
  • Sylvain Ardo Banbeto Gouroudja,
  • Henri Paul Ekobena Fouda

摘要

This work deals with the mathematical modelling of Typhoid fever disease dynamics using Caputo type fractional derivative. After the formulation of the model, we compute the basic reproduction number \(R_0\) and prove the local and global stability of the Typhoid-free equilibrium whenever \(R_0<1\) . For \(R_0>1\) , we prove that there exists only one endemic equilibrium which is globally asymptotically stable. Then, we prove existence and uniqueness of solution as well as its global stability using the Ulam-Hyers criterion. We finally perform numerical simulation to validate our theoretical results.