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We formulate an SIS model describing transmission of highland malaria inWestern Kenya. The host population is classified as children, age 1- 5 yearsand adults, above 5 years. The susceptibility and infectivity of an individualdepend on age class and residence. The large scale system with 6n equations is reduced into a compactform of 3n equations by a change ofvariables. Then 3n equations are vectorializedusing the matrix theory to get a one dimension, compact form of the system,equation in . Using Vidyasagar theorem 1, the graph of the reduced system is shown to bestrongly connected and the system is a monotone dynamical system. This meansthat circulation of malaria parasites among the species and among the patchesis strongly connected, hence transmission is sustained. We show that for then-dimensional age structured system thepositive orthant is positively invariant for all positive values of thevariables.

KEYWORDS

Highland Malaria, Differentiated Susceptibility and Infectivity, Monotone Dynamical Systems, Age Structure

Cite this paper

Wairimu, J. , Gauthier, S. and Ogana, W. 2014 Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes. Applied Mathematics, 5, 1535-1545. doi: 10.4236-am.2014.510147.





Autor: Josephine Wairimu, Sallet Gauthier, Wandera Ogana

Fuente: http://www.scirp.org/



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