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On the limits of the Volterra function in the Lyapunov method: the Anderson-May-Gupta model as a cautionary example

Abstract : The Volterra-type Lyapunov functions are an ubiquitous tool for establishing global stability in systems appearing in mathematical biology. We show, however, that no function of this type can be a Lyapunov function for the endemic equilibria of a classical intra-host model of malaria-the AMG model. More precisely, we give a sharp condition on the model parameters for this to be the case. This condition leaves out a large and biologically meaningful parameter range that will have to be addressed by a different method. We also present a set of three alternative arguments that enlarge the range of parameters for which global stability can be obtained-including parameter ranges that are relevant to malaria.
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https://hal.inria.fr/hal-03750220
Contributor : Abderrahman Iggidr Connect in order to contact the contributor
Submitted on : Thursday, August 11, 2022 - 10:36:24 PM
Last modification on : Saturday, August 13, 2022 - 3:20:35 AM

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Abderrahman Iggidr, Max O Souza. On the limits of the Volterra function in the Lyapunov method: the Anderson-May-Gupta model as a cautionary example. Journal of Mathematical Analysis and Applications, Elsevier, inPress, ⟨10.1016/j.jmaa.2022.126465⟩. ⟨hal-03750220⟩

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