Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis

Abstract

In this study, the authors proposed a nonlinear deterministic model and stability analysis for the transmission dynamics of chewing khat. The model’s solution is proved to be positive and bounded, and the basic reproduction number ( R 0 ) is calculated using the next-generation matrix method. Following that, the authors have looked at the local and global stability of the model’s khat-free and endemic equilibrium points. When R 0 < 1 , the chewing khat-free equilibrium point is locally and globally asymptotically stable, whereas when R 0 > 1 , the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.

New fractional derivative model for Khat chewing dynamics

“…We determine the equilibrium points of the fractional derivative system (2.11) by equating its right-hand side to zero. Solving the resulting algebraic system, we obtain two equilibrium points, namely, Khat Chewing-Free Equilibrium Point ( 𝑃 1 ), and Chewing Khat Endemic Equilibrium Point ( 𝑃 * ), which are the same as the equilibrium points given in [20] and are defined as…”