Global analysis of a shistosomiasis infection with biological control

Mouhamadou Diaby 1, 2 Abderrahman Iggidr 3, 1, * Abdou Sène 2 Mamadou Sy 2
* 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
LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
3 EDP - Equations aux dérivées partielles
IECL - Institut Élie Cartan de Lorraine
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.
Document type :
[Research Report] RR-8148, INRIA. 2013, pp.24
Contributor : Abderrahman Iggidr <>
Submitted on : Friday, December 27, 2013 - 9:07:08 PM
Last modification on : Saturday, September 17, 2016 - 1:09:36 AM


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  • HAL Id : hal-00758009, version 2


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




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