Effect of quarantine on transmission dynamics of Ebola virus epidemic: a mathematical analysis

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 $$F^{0}$$ , $$F^{1}$$ and the threshold parameter $${\mathcal {R}}_{0}$$ of the model are evaluated. An analytic stability analysis of equilibrium points with the help of $${\mathcal {R}}_{0}$$ is performed. It is observed that $$F^{0}$$ is both locally and globally asymptotically stable when $${\mathcal {R}}_{0}$$ is strictly less than unity which means that there will be no epidemic. Moreover, $$F^{0}$$ is not stable and $$F^{1}$$ is both locally and globally asymptotically stable when $${\mathcal {R}}_{0}$$ 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 $$F^{1}$$ for different quarantine levels is also presented. We have studied the effect of different quarantine coverage levels on threshold parameter $${\mathcal {R}}_{0}$$ 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.