Multiple Optimal Control Strategies in a Vector-Borne Reaction-Diffusion Model

Abstract

Mathematical models aim to help predictions and possible contention of disease spread, in particular vector-borne diseases. We have been working with a reaction-diffusion model that considers spatial movement of humans and vectors, with local contact transmission of Zika virus. Control measures, namely vaccination, human and vector contact reduction and vector elimination, are introduced in order to characterize an optimal strategy that minimizes the costs associated with infections and interventions. The optimal control characterization for each control variable is obtained in terms of state and adjoint equations. Numerical simulations are carried out using data for the initial 2015 Zika out break in the state of Rio Grande do Norte in Brazil. Several scenarios are simulated and analyzed in terms of number of new infections and costs, showing that the optimal control application is successful.