# Analysis, simulation and optimal control of a SEIR model for Ebola virus with demographic effects

## TL;DR

This paper develops and analyzes a SEIR mathematical model for Ebola virus, incorporating demographic effects, and evaluates control strategies like vaccination through simulations and case study of Liberia.

## Contribution

It introduces a SEIR model with demographic effects for Ebola and analyzes its equilibria and control strategies, including vaccination, with real-world application.

## Key findings

- Demographic effects influence Ebola outbreak dynamics.
- Vaccination can effectively control the virus spread.
- Model simulations align with theoretical predictions.

## Abstract

Ebola virus is one of the most virulent pathogens for humans. We present a mathematical description of different Susceptible-Exposed-Infectious-Recovered (SEIR) models. By using mathematical modeling and analysis, the latest major outbreak of Ebola virus in West Africa is described. Our aim is to study and discuss the properties of SEIR models with respect to Ebola virus, the information they provide, and when the models make sense. We added to the basic SEIR model demographic effects in order to analyze the equilibria with vital dynamics. Numerical simulations confirm the theoretical analysis. The control of the propagation of the virus through vaccination is investigated and the case study of Liberia is discussed in detail.