Modeling repellent-based interventions for control of vector-borne diseases with constraints on extent and duration

We study a simple model for a vector-borne disease with control intervention based on clothes and household items treated with mosquito repellents, which has constraints on the extent (population coverage) and on the time duration reflecting technological and physical properties. We compute first, the viability kernel of initial data of the model for which exists an optimal control that maintains the infected host population below a given cap for all future times. Second, we use the viability kernel to compute the set of initial data of the model for which exists an optimal control that brings this population below the cap in a time period not exceeding the intervention's duration. We discuss applications of this framework in predicting and evaluating the performance of control interventions under the given type of constraints.