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hal-00758009, version 1

Global analysis of a shistosomiasis infection with biological control

Mouhamadou Diaby () a12, Abderrahman Iggidr (Author to contact preferably) a1, Mamadou Sy () b2, Abdou Sène () c2

N° RR-8148 (2012)

Abstract: In this paper, the analysis of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species is studied by constructing Lyapunov functions and using a Krasnoselkii sublinearity trick. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We obtain the global stability of the disease-free equilibrium E0 when R0 ≤ 1 and we prove the existence and local stability of the endemic equilibrium E∗ when R0 > 1.

  • a –  INRIA Nancy-Grand Est
  • b –  Université Gaston Bergé (Saint-Louis, Sénégal)
  • c –  Université Gaston Bergé (Saint-Louis, Sénégal)ersité Gaston Bergé (Saint-Louis, Sénégal)
  • 1:  MASAIE (INRIA Nancy - Grand Est / LMAM)
  • INRIA – Université Paul Verlaine - Metz – CNRS : UMR7122 – Université de Lorraine
  • 2:  Laboratoire d'Analyse Numérique et Informatique [Sénégal] (LANI)
  • Université Gaston Berger de Saint-Louis
  • hal-00758009, version 1
  • oai:hal.inria.fr:hal-00758009
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  • Submitted on: Tuesday, 27 November 2012 19:34:18
  • Updated on: Wednesday, 28 November 2012 19:43:23