Efficacy of Isolation as a Control Strategy for Ebola Outbreaks in Combination with Vaccination

Abstract

In this research work, we have developed and analyzed a deterministic epidemiological model with a system of nonlinear differential equations for controlling the spread of Ebola virus disease (EVD) in a population with vital dynamics (where birth and death rates are not equal). The model examines the disease transmission dynamics with isolation from exposed and infected human class and effect of vaccination in susceptible human population through stability analysis and bifurcation analysis. The model exhibits two steady state equilibria, namely, disease-free and endemic equilibrium. Next generation matrix method is used to find the expression for [Formula: see text] (the basic reproduction number). Local and global stability of diseases-free equilibrium are shown using nonsingular M-matrix technique and Lyapunov’s theorem, respectively. The existence and local stability of endemic equilibrium are explored under certain conditions. All numerical data entries are supported by various authentic sources. The simulation study is done using MATLAB code 45 which uses Runge–Kutta method of fourth order and we plot the time series and bifurcation diagrams which support our analytical findings. Stability analysis of the model shows that the disease-free equilibrium is locally as well as globally asymptotically stable if [Formula: see text] and endemic equilibrium is locally asymptotically stable in absence of vaccination if [Formula: see text]. Using central manifold theorem, the presence of transcritical bifurcation for a threshold value of the transmission rate parameter [Formula: see text] when [Formula: see text] passes through unity and backward bifurcation (i.e. transcritical bifurcation in opposite direction) for some higher value of [Formula: see text] are established. Our simulation study shows that isolation of exposed and infected individuals can be used as a more effective tool to control the spreading of EVD than only vaccination.