The model was governed by a system of ordinary differential equations; with the total population sub-divided into Susceptible individuals (S), Latently individuals (L), Infected undetected individuals (Iu) , Infected detected individuals (Id) and Recovered individuals (R). Theory of positivity and boundedness was used to investigate the wellposedness of the model. Equilibrium solutions were investigated analytically. The basic reproduction number (R0) was calculated using the next generation method. Bifurcation analysis and global stability of the model were carried out using centre manifold theory and Lyapunov functions respectively. The effects of parameters such as Progression rate of infected individual to infectious individual (τ1), Effective contact rate (β), Modification parameter (θ), Slow progressor (ε), Endogenous reactivation rate (α), Detection rate of infected undetected individual (r), Recovery rate of infected detected individual due to treatment (τ2) and Recovery rate of infected undetected individual due to treatment (τ3) on R0 were explored through sensitivity analysis. To reduce the burden of Ebola virus disease in the population the following parameters, τ1, β, θ, ε, α, r, τ2, and τ3 play a significant role in the spread of it in the population. Numerical simulation is analyzed by MAPLE 18 software using embedded RungeKutta method of order (4) which shows the dynamical spread of Ebola virus disease.
