A fractal–fractional model of Ebola with reinfection

Abstract

In this article, we have studied the dynamics of the Ebola virus disease by means of fractional differentiation combined with a fractal dimension. It has been shown explicitly that the Ebola model is positively invariant. The fixed point theorem procedures check the solution’s existence and uniqueness to the model using the Mittag-Leffler kernel. The stability of the Ebola fractal–fractional model is studied using the Hyers–Ulam stable analysis. The numerical simulation for the trajectories of the proposed model is obtained using Lagrangian interpolation. Also, the numerical sensitivity analysis of the model is presented. For instance, a reduction in the rate of human-to-human contact results in a decline in the rate of infection, implying that the disease at a point will die out. Again, an increase in the loss of immunity rate to unity leads to a massive spread of the Ebola disease in the population. The findings in our work depict that we can achieve an Ebola-free state should the health sector give more education on maintaining a strong immune system and reducing human-to-human contact, especially during outbreaks of the Ebola disease, using measures like isolation and quarantine. Finally, using the fractal–fractional operator, we observed that any amount of memory variation and repetition in the outbreak of the disease influences the spread of the Ebola disease.