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Global analysis of a schistosomiasis infection model with biological control

Mouhamadou Diaby 1, 2 Abderrahman Iggidr 1, 3 Mamadou Sy 2 Abdou Sene 2
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
2 LANI
LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
Abstract : In this paper, the global stability of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mam-malian host and a competitor snail species is studied by constructing Lya-punov functions and using properties of K monotone systems. We derive the basic reproduction number R 0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R 0 . We show that the disease can be eradicated when R 0 ≤ 1. In the case where R 0 > 1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. This mathematical analysis of the model gives insight about the epidemiological consequences of the introduction of a competitor resistant snail species.
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Mouhamadou Diaby, Abderrahman Iggidr, Mamadou Sy, Abdou Sene. Global analysis of a schistosomiasis infection model with biological control. Applied Mathematics and Computation, Elsevier, 2014, 246, pp.731 - 742. ⟨10.1016/j.amc.2014.08.061⟩. ⟨hal-01086737⟩

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