Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

TL;DR

This paper models the 2014 Ebola outbreak in Liberia, validates the model with data, introduces vaccination strategies, and applies optimal control to assess vaccination impact on virus spread.

Contribution

It presents a new mathematical model including vaccination effects and employs optimal control techniques to optimize vaccination strategies during the Ebola outbreak.

Findings

Vaccination reduces infection numbers over time.

Optimal control identifies effective vaccination strategies.

Model validation aligns well with observed data.

Abstract

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leonne and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multi-shooting method.