Global stability analysis of a metapopulation SIS epidemic model

Abderrahman Iggidr 1, 2, * Gauthier Sallet 1, 2 Berge Tsanou 1, 3
* Corresponding author
1 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : The conjecture of Arino and van den Driessche (2003) that a SIS type model in a mover- stayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number R0 ≤ 1, then the disease free equilibrium is globally asymptotically sta- ble. If R0 > 1, then there exists a unique endemic equilibrium which is globally asymptotically stable on the nonnegative orthant minus the stable manifold of the disease free equilibrium.
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Abderrahman Iggidr, Gauthier Sallet, Berge Tsanou. Global stability analysis of a metapopulation SIS epidemic model. Mathematical Population Studies, Taylor & Francis (Routledge), 2012, 19 (3), pp.115-129. ⟨hal-00648041⟩

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