Abstract:
Many mathematical models for the
spread of infectious diseases in a population assume homogeneous mixing, but due to spatial distribu-
tion, there exist distinct patches with unique disease dispersion dynamics, especially if between patch mixing due to travel
and migration
is limited. In th
is paper, three levels of disease status in a -
patch metapopulation was studied using a simple SIR
-
HIV epidemic model
in a one dimensional nearest neighbour coupling lattice. The basic reproductive ratio, which is a function of coupling strength,
is
shown to affect stability characteristics of equilibrium points. The disease free equilibrium (DFE) is globally asymptotically stable irrespective of the value of
but the
stability of the endemic equilibrium point (EEP) depends on the coupling strength
. It was found that
at the critical value of coupling strength ≥
0
.
67
, the subpopulations dynamics are synchronized while for
≤
0
.
3
the subpopulation
dynamics are independent
. Patch
isolation strategy for the control of HIV dispersion requires
a
critical coupling strength of ≤
0
.
15
.
This interaction restriction reduces
to values less than one, and the disease will be eliminated, making isolation effective.
Demographic and epidemiological parameters of Vihiga County in Kenya were used in the study
