Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes
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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.
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.
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