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Formulation of a vector SIS malaria model in a patchy environment with two age classes

Josephine Wairimu 1 Gauthier Sallet 2, 3 Wandera Ogana 1
2 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 formulate an SIS model describing transmission of highland malaria in Western Kenya. The host population is classified as children, age 1-5 years and adults, above 5 years. The susceptibili-ty and infectivity of an individual depend on age class and residence. The large scale system with 6n equations is reduced into a compact form of 3n equations by a change of variables. Then 3n equations are vectorialized using the matrix theory to get a one dimension, compact form of the system, equation in n 3  . Using Vidyasagar theorem [1], the graph of the reduced system is shown to be strongly connected and the system is a monotone dynamical system. This means that circula-tion of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for the n-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.
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Josephine Wairimu, Gauthier Sallet, Wandera Ogana. Formulation of a vector SIS malaria model in a patchy environment with two age classes. Applied Mathematics, Scientific Research Publishing, 2014, 5 (10), pp.1535 - 1545. ⟨10.4236/am.2014.510147⟩. ⟨hal-01085952⟩

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