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Stability analysis of within-host parasite models with delays.

Abderrahman Iggidr 1, * Joseph Mbang 1, 2 Gauthier Sallet 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 provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability.
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Abderrahman Iggidr, Joseph Mbang, Gauthier Sallet. Stability analysis of within-host parasite models with delays.. Mathematical Biosciences, Elsevier, 2007, 209 (1), pp.51-75. ⟨10.1016/j.mbs.2007.01.008⟩. ⟨inria-00552051⟩

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