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Epidemiological Models and Lyapunov Functions

A. FallA. IggidrG. SalletJ. J. Tewa — 2010

Mathematical Modelling of Natural Phenomena

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...

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