this Paper we formulate a mathematical model of dengue virus transmission in
the human body to monitor the effects of migratory population and some control
strategies at aquatic and adult stages of vector (mosquito). The model has a
locally asymptotically stable disease-free equilibrium (DFE) whenever a certain
epidemiological threshold, known as the basic reproduction number (R0), is less
than unity. It is also shown, using a Lyapunov function and Lasalle Invariance
Principle that the DFE of the dengue model is globally-asymptotically stable
(GAS) whenever the reproduction number (R0) is less than unity. The model has a
locally-asymptotically stable endemic equilibrium point (EEP) whenever R0>1.
With the help of Lyapunov function and Lasalle Principle (Goh-Volterra type),
by considering special case, the EEP of the model is shown to be GAS whenever R0>1. The model simulations reveals that the migratory infected individuals
increases the burden of the dengue disease and also precautionary measures at
the aquatic and adult stages decrease the number of new cases of dengue virus.
Numerical simulation indicates that if we take the precautionary measures
effectively then it would be more effective then even giving the treatment to
the infected individuals.