A simple mathematical model for Ebola in Africa

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Ebola virus disease (EVD) outbreaks in Africa are recurrent and persistent.
• Factors such as bush meat consumption, funeral practices, and environmental contamination are suspected contributors.

Purpose of the Study:

• To investigate if bush meat consumption, funeral practices, and environmental contamination explain the persistence of EVD outbreaks.
• To develop and analyze a mathematical model incorporating direct and indirect transmission routes, including environmental virus presence.

Main Methods:

• Development of a compartmental SIR-type mathematical model for EVD transmission.
• Analysis of model equilibria to determine stability conditions (local and global).
• Design and implementation of a nonstandard finite difference scheme for numerical simulations.

Main Results:

• The full model, including environmental virus presence, exhibits a single, locally asymptotically stable endemic equilibrium.
• In the absence of environmental virus shedding, the disease stabilizes globally at an endemic equilibrium.
• The number of infectious individuals is higher in the full model compared to the model without environmental virus presence.

Conclusions:

• Bush meat consumption, funeral practices, and environmental contamination are significant factors in the recurrence and persistence of Ebola outbreaks.
• The mathematical model provides insights into EVD dynamics, highlighting the role of environmental virus reservoirs.
• The designed numerical scheme accurately preserves the model's epidemiological dynamics.