| Abstract: |
| This presentation concerns a late-season model of a West Nile virus epidemic that includes transmission between bird hosts and mosquito vectors, mosquito life stages, and pesticide dynamics. Our model describes three mosquito life stages; eggs, larvae, and adults, and three pesticides; two types of larvicide and one adulticide. The basic reproduction number for the model epidemic is analyzed in the absence of control, and impulsive optimal control problems are constructed. Objective functions are designed to balance the cost of the insecticide application schedule with the benefit of (1) vector control: reducing the number of mosquitoes or (2) disease control: reducing the disease burden. The resulting impulsive optimal control problems are then reformulated as nonlinear optimization problems in order to derive necessary conditions for the characterization of optimal controls. Numerical simulations are used to address three questions: How does the control and its impact on the system vary with the objective type? Is it beneficial to optimize the treatment timing? How does the control and its impact on the population vary with the type of pesticide used? |
|