Local and Global Stability Analysis of the Disease-Free Equilibrium in A Fractional-Order Ebola Virus Transmission Model

Abstract

A non-linear fractional-order mathematical model describing the transmission dynamics of Ebola virus disease is developed. The model consists of a system of fourteen non-linear fractional differential equations of order 𝛼. The non-negativity of solutions is established, demonstrating that the model is biologically meaningful and mathematically well-posed. The disease-free equilibrium points are derived, and their stability properties are investigated through the construction of appropriate Lyapunov functions. The results show that the disease-free equilibrium points are both locally and globally asymptotically stable. Numerical simulations are performed to illustrate the theoretical results and to further examine the dynamical behavior of the model.