Mathematical analysis of in-host Ebola virus infection dynamics model with sensitivity analysis

Abstract

Ebola virus (EBOV) causes a haemorrhagic and lethal Ebola disease disastrous to human beings, which is transmitted by contact of body fluids of infected animals and humans. Presently, there are no therapies for the disease. In this paper, a mathematical model is proposed to investigate the in-vivo dynamics of EBOV infection with sensitivity analysis. A system of five non-linear ordinary differential equations constitutes the model, from which the basic reproduction number, R₀ is calculated using the next generation matrix method. The parameter R₀ is employed to analyze global stability of disease-free and endemic equilibria. Using the Metzler matrix operator, the results indicate that the disease-free equilibrium point is globally asymptotically stable provided that R₀ < 1, which implies that the disease disappears from the host after some period of time. With Lyapunov Stability Theory and LaSalle Invariant Principle, the results indicate that the endemic equilibrium point is globally asymptotically stable provided that R₀ > 1, which implies that the disease persists in the host. Sensitivity analysis of the basic reproduction number pertaining to the model parameters is achieved using forward normalized sensitivity index method. The results indicate that the parameters for infection rate, production rate of uninfected target cells and virus replication rate are positively sensitive. On the other hand, the parameters for natural death rate of target cells and natural death rate of the virus are negatively sensitive, implying that the basic reproduction number decreases as the parameters increase and vice versa. Besides, it is shown that the parameter for the infection rate is the most sensitive one while the parameter for the virus reproduction rate is the least sensitive one. Numerical simulations are used to validate the analytical results. The results suggest implementation of deliberate control measures to eradicate EBOV disease by considering sites in the model to which the most sensitive parameters are affiliated.