Global analysis of a shistosomiasis infection with biological control

Mouhamadou Diaby 1, 2 Abderrahman Iggidr 1, * Abdou Sène 2 Mamadou Sy 2
* Corresponding author
2 LANI
LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
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.
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Reports
[Research Report] RR-8148, 2013, pp.24


https://hal.inria.fr/hal-00758009
Contributor : Abderrahman Iggidr <>
Submitted on : Friday, December 27, 2013 - 9:07:08 PM
Last modification on : Wednesday, October 29, 2014 - 10:10:23 AM

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Mouhamadou Diaby, Abderrahman Iggidr, Abdou Sène, Mamadou Sy. Global analysis of a shistosomiasis infection with biological control. [Research Report] RR-8148, 2013, pp.24. <hal-00758009v2>

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