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Metapopulation SIS epidemic model

Abderrahman Iggidr 1, * Gauthier Sallet 1 Berge Tsanou 1
* 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 : We consider a metapopulation model with $n$ patches. The migration model is with residents and travelers. The epidemic model is of SIS type. We confirm the conjecture of Arino and van den Driessche. We prove that if $\mathcal R_0 \leq 1$ then the disease free equilibrium is globally asymptotically stable. If $\mathcal R_0 >1$ we prove that there exists a unique endemic equilibrium which is globally asymptotically stable on the nonnegative orthant except the disease free equilibrium.
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https://hal.inria.fr/inria-00595397
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Submitted on : Tuesday, May 24, 2011 - 4:40:16 PM
Last modification on : Thursday, March 5, 2020 - 4:53:39 PM
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Abderrahman Iggidr, Gauthier Sallet, Berge Tsanou. Metapopulation SIS epidemic model. 9th African Conference on Research in Computer Science - CARI'2008, CARI, Oct 2008, Rabat, Morocco. pp.51-59. ⟨inria-00595397⟩

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