Fractional order mathematical modeling of typhoid fever disease

Abstract

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.

Keywords

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