Abstract
In this paper, a nonlinear model called susceptible-exposed-infected-quarantined-recovered is developed to study the transmission of Ebola virus disease (EVD). In the proposed model, an additional class of quarantined humans is incorporated to investigate the impact of quarantine strategy for exposed population. A comprehensive mathematical analysis of this model is carried out to understand the dynamical behavior of EVD. Equilibrium points F0, F1 and the threshold parameter R0 of the model are evaluated. An analytic stability analysis of equilibrium points with the help of R0 is performed. It is observed that F0 is both locally and globally asymptotically stable when R0 is strictly less than unity which means that there will be no epidemic. Moreover, F0 is not stable and F1 is both locally and globally asymptotically stable when R0 is strictly greater than unity which indicates a uniform spread of disease among individuals. Global stability of both equilibria is established by employing theory of Lyapunov functions. To validate theoretical results thus obtained, the system of ODEs is solved by employing three well-known different numerical methods such as Euler method, Runge-Kutta method of order 4 (RK4), and the nonstandard finite difference (NSFD) method. It is worth mentioning that the Euler and RK4 numerical schemes converge conditionally, whereas the proposed NSFD scheme converges unconditionally and is dynamically consistent with the continuous model. A quantitative analysis of the proposed model at endemic point F1 for different quarantine levels is also presented. We have studied the effect of different quarantine coverage levels on threshold parameter R0 to draw our conclusions. Numerical results drawn using MATLAB validate our claim that EVD could be eradicated faster if quarantine measures with proper awareness at various coverage levels are adopted. Global asymptotical stability of equilibrium points is shown by 3D plots. Finally, the joint variability of populations is executed to assess the impact of quarantine measures on the transmission dynamics of a disease.