Deterministic Models in Dengue Transmission Dynamics
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
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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