Analytical and numerical investigations of optimal control techniques for managing Ebola virus disease

Abstract

Ebola virus disease, often referred to as Ebola hemorrhagic fever, is one of the deadliest viral infections, posing a severe global health threat. It typically originates from human contact with domestic or wild animals and spreads through direct and indirect human contact, making containment highly challenging. Managing and controlling the spread of Ebola disease remains a significant challenge in epidemic response efforts. This study introduces a novel compartmental model to examine Ebola disease transmission dynamics and the effectiveness of control strategies. We conduct a mathematical analysis to ensure the model’s well-posedness and explore its stability properties. The theoretical results are verified using three numerical methods: the Euler’s method, the fourth-order Runge–Kutta method, and the non-standard-finite-difference method. Furthermore, the impact of time-invariant vaccination and quarantine rates on the epidemic is analyzed using the non-standard-finite-difference approach. A sensitivity analysis is conducted on the model to identify the most influential parameters affecting disease transmission. Additionally, we formulate an optimal control problem to identify effective, time-dependent strategies for Ebola vaccination and quarantine measures. As a novel contribution, our findings emphasize the potential of these control strategies in reducing both infection rates and associated costs, with a particular focus on the most reliable non-standard finite difference scheme. The application of forward and backward-in-time non-standard finite difference method ensures numerical stability and preserves essential biological properties. Numerical simulations demonstrate that a combination of effective vaccination and quarantine measures, and public awareness can accelerate the control of Ebola virus disease. Overall, this study provides a comprehensive approach to modeling, analyzing, and controlling Ebola virus disease by integrating advanced mathematical techniques with practical disease management strategies.