Deterministic Models in Dengue Transmission Dynamics - Abu Bakar, Mohd Rizam; Mohammed, Salisu Garba; Ibrahim, Noor Akma; Monsi, Mansor (Institute for Mathematical Research, 2008)
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.