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Epidemiological models and Lyapunov functions

Abstract : 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 R0 \leq 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant.
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A. A. Fall, Abderrahman Iggidr, Gauthier Sallet, Jean-Jules Tewa. Epidemiological models and Lyapunov functions. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2007, 2 (1), pp.62 - 83. ⟨10.1051/mmnp:2008011⟩. ⟨inria-00596236⟩

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