Caputo Fractional Order Ebola Model with Double Saturated Incidence Rates and Vaccination

Abstract

The emergence of Ebola Virus Disease (EVD) prompted significant efforts by many countries, particularly across Africa, to develop strategies for addressing the ensuing uncertainties. EVD, stemming from any of the four species within the Filoviridae family, serves as the focal point of investigation in this thesis. Herein, we constructed a mathematical model incorporating susceptible (S), infected (I), recovered (R), and deceased (E) compartments to examine the spread of the Ebola virus with double-saturated incidence rates using the Caputo fractional order derivative. The vaccination component was introduced to assess its impact on disease dynamics and explore potential control strategies, leveraging natural immunity. We derived the feasible equilibria of the model and established conditions for boundedness. Using the next-generation matrix, we determined the fundamental reproduction number to direct the stability analysis of disease-free and endemic equilibrium points at both local and global levels. Numerical results are presented to clarify specific model behaviors, complemented by simulations that validate mathematical analyses.