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.