Ebola epidemic model with dynamic population and memory

Abstract

The recent outbreaks of Ebola encourage researchers to develop mathematical models for simulating the dynamics of Ebola transmission. We continue the study of the models focusing on those with a variable population. Hence, this paper presents a compartmental model consisting of 8-dimensional nonlinear differential equations with a dynamic population and investigates its basic reproduction number. Moreover, a dimensionless model is introduced for numerical analysis, thus proving the disease-free equilibrium is locally asymptotically stable whenever the threshold condition, known as a basic reproduction number, is less than one. Finally, we use a fractional differential form of the model to sufficiently fit long time-series data of Guinea, Liberia, and Sierra Leone retrieved from the World Health Organization, and the numerical results demonstrate the performance of the model.