Mathematical modelling and nonstandard finite scheme analysis for an Ebola model transmission with information and voluntary isolation

Abstract

A major Ebola outbreak occurs in West Africa since March 2014, being the deadliest epidemic in history. On August 2014, the World Health Organization (WHO) declared the outbreak public health emergency of international concern. In this work, we propose an epidemic model to study the transmission dynamics of Ebola virus disease (EVD) with high- and low-risk susceptible populations. Our aim is to analyse and assess the impacts of positive and negative information conveyed on the field about EVD spreading. The model considers two different groups of susceptible individuals depending on the level of information about the disease spreading. We provide a theoretical study of the model, compute the disease-free equilibrium (DFE) and derive the basic reproduction number that determines the extinction and the persistence of the disease. Also, we compute equilibria and study their stability. More precisely, we show that the DFE is globally asymptotically stable whenever . Conversely, when is greater than one, the DFE becomes unstable and a unique endemic equilibrium arises which is locally asymptotically stable. These results are obtained through the construction of suitable Lyapunov functions combined with Lyapunov–LaSalle techniques and the search for the eigenvalues of the Jacobian matrix, respectively. We design a nonstandard finite difference scheme, which preserves the essential properties of the continuous system. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Furthermore, we provide numerical simulations to support the analytical results.