Mathematical Analysis of the Role of Detection Rate on Dynamical Spread of Ebola Virus Disease

Abstract

In this paper, a non-linear mathematical model of the Ebola virus disease with detection rate is proposed and analyzed. The whole population under consideration is divided into five compartments e.g. susceptible, latently infected, infected undetected, infected detected, and recovered to study the transmission dynamics of the Ebola virus disease. Based on the immunity level, susceptible individuals move to exposed class or directly to infected detected class once they come into contact with an infective. This has been incorporated through the progression rate which is slow. The equilibria of the model and the basic reproduction number R0 are computed. It is observed that the disease-free equilibrium of the model is locally asymptotically stable when R0<1. The model exhibits forward bifurcation under certain restrictions on parameters, which indicate that the model has a single endemic equilibrium for R0<1. This suggests that an accurate estimation of parameters and the level of control measures are required to reduce the infection prevalence of the Ebola virus in the endemic region and just R0<1 is enough to eliminate the disease from the population. R0 needs to be lowered much below one to confirm the global stability of the disease-free equilibrium. Numerical simulation is performed to demonstrate the analytical results. It is found that the increase in the rate of detection rate leads to a decrease in the threshold value of R0. Numerical simulations have been carried out to support the analytic results.