Fractional order mathematical modeling of typhoid fever disease

Muhammad Sinan, Kamal Shah, Poom Kumam, Ibrahim Mahariq, Khursheed J. Ansari, Zubair Ahmad, Zahir Shah

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


This manuscript is devoted to focusing on the modeling and numerical solution of the dynamical model of Typhoid Fever. We use the Atangana–Baleanu operator with the Mittag–Leffler function in Caputo sense to study the behavior of the model. Both local and global stability analysis are studied. Further, for global stability, we use the Lyapunov function at both disease-free and endemic equilibrium points. As a result, the model of Typhoid fever is locally and globally stable around disease-free and endemic equilibrium points and also possesses a unique solution. The strong numerical Adams–Bashforth method is used for the numerical solution and graphical representation to justify the results. It is observed that increasing the interaction rate among the susceptible and infected population increases basic reproduction number which means that the spread of disease increases by increasing interaction rate and disease transmission can be controlled by decreasing the interaction.

Original languageEnglish
Article number105044
JournalResults in Physics
Publication statusPublished - Jan 2022
Externally publishedYes


  • Adam Bashforth method
  • Atangana–Baleanu operator
  • Existence and uniqueness
  • Lyapunov stability
  • Mathematical modeling
  • Mittag–Leffler function
  • Next generation matrix


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