Application of three controls optimally in a vector-borne disease – a mathematical study

We have proposed and analyzed a vector-borne disease model with three types of controls for the eradication of the disease. Four different classes for the human population namely susceptible, infected, recovered and vaccinated and two different classes for the vector populations namely susceptible and infected are considered. In the first part of our analysis the disease dynamics are described for fixed controls and some inferences have been drawn regarding the spread of the disease. Next the optimal control problem is formulated and solved considering control parameters as time dependent. Different possible combination of controls are used and their effectiveness are compared by numerical simulation.

► An epidemic problem with vector-borne disease is proposed and analyzed.
► We apply three control parameters: vaccination, treatment and insecticide.
► The existence of the optimal controls are derived.
► Some simulation works are given.