Citation
Abu Bakar, Mohd Rizam and Mohammed, Salisu Garba and Ibrahim, Noor Akma and Monsi, Mansor
(2008)
Deterministic Models in Dengue Transmission Dynamics.
Math Digest : Research Bulletin Institute for Mathematical Research, 2 (1).
pp. 21-33.
ISSN 1985-2436
Abstract
Adeterministic model for monitoring the impact of
treatment on the transmission dynamics of dengue
in the human and vector populations is presented.
In addition to having a locally-asymptotically
stable disease-free equilibrium (OFE) whenever
the basic reproduction number is less than unity, it
is shown, llsing a Lyapunov function and LaSalle
Invariance Principle that the DFE of both
treatment~frcc and treatment model, in the absence
of dengue-induced 1ll00tality, IS globallyasymptotically
stable whenever the reproduction
number is less than unity. Each oftbe models has a
unique endemic equilibrium whenever its
reproduction number excceds unity. Numerical
simulations of thc model show that for high
treatment rates, the disease can be controled within
a community.
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