Math. Model. Nat. Phenom.
Volume 2, Number 1, 2007Epidemiology
|Page(s)||62 - 83|
|Published online||15 June 2008|
Epidemiological Models and Lyapunov Functions
INRIA Lorraine & Université Paul Verlaine, Metz LMAM (UMR CNRS 7122)
I.S.G.M.P. Bât A, Ile du Saulcy, 57045 Metz Cedex 01, France
2 Université de Saint-Louis, Sénégal
3 Université de Yaoundé, Cameroun
Corresponding author: email@example.com
We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio ≤ 1, then the disease free equilibrium is globally asymptotically stable. If > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant.
Mathematics Subject Classification: 34A34 / 34D23 / 34D40 / 92D30
Key words: nonlinear dynamical systems / global stability / Lyapunov methods / differential susceptibility models
© EDP Sciences, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.