Mathematical Analysis of a Large Scale Vector SIS Malaria Model in a Patchy Environment

Josephine Wairimu 1 Gauthier Sallet 2, 3 Wandera Ogana 1
1 School of Mathematics [Nairobi]
2 EDP - Equations aux dérivées partielles
IECL - Institut Élie Cartan de Lorraine
3 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 answer the stability question of the large scale SIS model describing transmission of highland malaria in Western Kenya in a patchy environment, formulated in [1]. There are two equilibrium states and their stability depends on the basic reproduction number, 0  [2]. If 0 1  ≤ , the dis-ease-free steady solution is globally asymptotically stable and the disease always dies out. If 0 1  > , there exists a unique endemic equilibrium which is globally stable and the disease persists. Application is done on data from Western Kenya. The age structure reduces the level of infection and the populations settle to the equilibrium faster than in the model without age structure.
Keywords : Highland Malaria Monotone Dynamical Systems Differentiated Susceptibility and Infectivity
Type de document :
Article dans une revue
Applied Mathematics, Scientific Research Publishing, 2014, 5 (13), pp.1913 - 1926. 〈10.4236/am.2014.513185〉
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https://hal.inria.fr/hal-01085955
Contributeur : Gauthier Sallet <>
Soumis le : vendredi 21 novembre 2014 - 14:56:08
Dernière modification le : jeudi 11 janvier 2018 - 06:26:21
Document(s) archivé(s) le : vendredi 14 avril 2017 - 19:15:19

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Josephine Wairimu, Gauthier Sallet, Wandera Ogana. Mathematical Analysis of a Large Scale Vector SIS Malaria Model in a Patchy Environment. Applied Mathematics, Scientific Research Publishing, 2014, 5 (13), pp.1913 - 1926. 〈10.4236/am.2014.513185〉. 〈hal-01085955〉

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