Conditions for endemicity

qualitative population dynamics in a long-running outbreak of Ebola virus disease

Authors

  • Olivia Brozek Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA Author
  • Matthew Glomski Department of Mathematics, Marist College, Poughkeepsie, NY,USA Author

DOI:

https://doi.org/10.30707/LiB4.1Brozek

Keywords:

Ebola virus disease, Compartmental model, Ordinary differential equations, Lyapunov stability

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 R0 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.

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Published

2017-01-01

Issue

Section

Research

How to Cite

Conditions for endemicity: qualitative population dynamics in a long-running outbreak of Ebola virus disease. (2017). Letters in Biomathematics, 4(1), 207-218. https://doi.org/10.30707/LiB4.1Brozek

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