Conditions for endemicity: qualitative population dynamics in a long-running outbreak of Ebola virus disease

Abstract

Ebola virus disease (EVD) struck West Africa in 2013–2016 in an epidemic of unprecedented scope, with over 28000 cases and 11000 fatalities in the affected region. The protracted duration of the outbreak – more than two-and-one-half years of active transmission – raises questions about the persistence of EVD. In this brief paper, we qualitatively examine conditions supporting long-running EVD epidemics via a susceptible – exposed – infectious – recovered – deceased-infectious differential equations model that incorporates births and non disease-related deaths. We define an ‘effective epidemiological population’ to include contagious individuals recently deceased from the disease. Under a constant effective epidemiological population condition, we consider the basic reproductive number $ \mathcal R _{0} $ and use Lyapunov function arguments to establish conditions in the parameter space supporting an exchange of stability from the disease-free equilibrium to an endemic equilibrium.

Keywords

• Ebola virus disease
• compartmental model
• ordinary differential equations
• Lyapunov stability