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

Josephine Wairimu, Sallet Gauthier, Wandera Ogana

INRIA, Metz and University of Lorraine, Metz, France.
School of mathematics, University of Nairobi, Nairobi, Kenya.

DOI: 10.4236/am.2014.510147                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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