Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis
Abayneh Kebede Fantaye, Zerihun Kinfe Birhanu
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 ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mi>R</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> </a:math> ) 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msub> <c:mrow> <c:mi>R</c:mi> </c:mrow> <c:mrow> <c:mn>0</c:mn> </c:mrow> </c:msub> <c:mo><</c:mo> <c:mn>1</c:mn> </c:math> , the chewing khat-free equilibrium point is locally and globally asymptotically stable, whereas when <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:msub> <e:mrow> <e:mi>R</e:mi> </e:mrow> <e:mrow> <e:mn>0</e:mn> </e:mrow> </e:msub> <e:mo>></e:mo> <e:mn>1</e:mn> </e:math> , the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.