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Githeko, A.K., Ayisi, J.M., Odada, P.K., Atieli, F.K., Ndenga, B.A., Githure, J.I. and Yan, G. (2006) Topography and Malaria Transmission Heterogeneity in Western Kenya Highlands: Prospects for Focal Vector Control. Malaria Journal, 5, 107. http://dx.doi.org/10.1186/1475-2875-5-107

has been cited by the following article:

• TITLE: Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

  AUTHORS: Josephine Wairimu, Sallet Gauthier, Wandera Ogana

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

  JOURNAL NAME: Applied Mathematics, Vol.5 No.10, June 6, 2014

  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 susceptibility 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 . 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 circulation of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for then-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.