A mathematical model on the impact of awareness and traditional medicine in the control of Ebola: case study of the 2014–2016 outbreaks in Sierra Leone and Liberia

Abstract

In the control of infectious diseases worldwide, awareness of the population occupies a prominent place. In Africa, there has been a long standing rivalry between traditional medicine and modern medicine. Any disease control strategy must take into account disease-oriented education, as this has a direct influence on the choice of treatment type to follow. In this work, we present a mathematical model that takes into consideration not only public health awareness but also the significant contribution of traditional medicine to the Ebola treatment effort. This study uses data from the 2014 – 2016 Ebola outbreaks in Sierra Leone and Liberia. Theoretically, we show that our model exhibits a trans-critical bifurcation at $\mathcal{R}_{c}=1$ and a backward bifurcation phenomenon whenever $\mathcal{R}_{c}^{c}<\mathcal{R}_{c}< 1$. While the disease persists when $\mathcal{R}_{c}>1$. In addition, a threshold number $\mathcal{T}_{0}$, is obtained which ensures the global asymptotic stability of the disease-free equilibrium when its value is less than one. Numerically, it is shown that the number of hospitalized infected cases increases more rapidly than the number of infected cases treated by traditional healers in both countries, suggesting that people have a high tendency to visit hospitals than visiting traditional healers. Our analysis reveals that during an Ebola outbreak, awareness messages should target the susceptible population for behavior change in order to mitigate the spread of the disease. Calibrating the model, it fits well the weekly cumulative cases in Sierra Leone and Liberia, and their corresponding estimated control reproduction numbers are $0.5725$ and $0.8340$, respectively.