Geodesic
Epidemiological Models and Lyapunov Functions
A. Fall1, 2 ; A. Iggidr1 ; G. Sallet1 ; J. J. Tewa1, 3
1 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
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 1, pp. 62-83.

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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.
DOI : 10.1051/mmnp:2008011

A. Fall 1, 2 ; A. Iggidr 1 ; G. Sallet 1 ; J. J. Tewa 1, 3

1 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 
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     title = {Epidemiological {Models} and {Lyapunov} {Functions}},
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A. Fall; A. Iggidr; G. Sallet; J. J. Tewa. Epidemiological Models and Lyapunov Functions. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 1, pp. 62-83. doi : 10.1051/mmnp:2008011. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008011/

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