TITLE:
Mathematical Analysis of a Large Scale Vector SIS Malaria Model in a Patchy Environment
AUTHORS:
Josephine Wairimu, Sallet Gauthier, Wandera Ogana
KEYWORDS:
Highland Malaria, Differentiated Susceptibility and Infectivity, Monotone Dynamical Systems
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
10,
2014
ABSTRACT: We answer the stability question of the large scale
SIS model describing transmission of highland malaria in Western Kenya in a
patchy environment, formulated in [1]. There are two equilibrium states and their
stability depends on the basic reproduction number, Ro[2]. If Ro ≤1, the disease-free steady solution is
globally asymptotically stable and the disease always dies out. If Ro >1, there exists a unique endemic equilibrium
which is globally stable and the disease persists. Application is done on data
from Western Kenya. The age structure reduces the level of infection and the
populations settle to the equilibrium faster than in the model without age
structure.