Formulation of a vector SIS malaria model in a patchy environment with two age classes - Archive ouverte HAL Access content directly
Journal Articles Applied Mathematics Year : 2014

Formulation of a vector SIS malaria model in a patchy environment with two age classes

(1) , (2, 3) , (1)
1
2
3

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 susceptibili-ty 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 n 3  . 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 circula-tion of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for the n-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.
Fichier principal
Vignette du fichier
AM_2014060614005287.pdf (800.2 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01085952 , version 1 (21-11-2014)

Identifiers

Cite

Josephine Wairimu, Gauthier Sallet, Wandera Ogana. Formulation of a vector SIS malaria model in a patchy environment with two age classes. Applied Mathematics, 2014, 5 (10), pp.1535 - 1545. ⟨10.4236/am.2014.510147⟩. ⟨hal-01085952⟩
332 View
180 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More