A model for a vector-borne disease with control based on mosquito repellents: A viability analysis

Abstract

We investigate a model for a vector-borne disease of susceptible-infected-removed type for the hosts in the presence of control measures and state constraints. The control is based on the use of textiles and household items treated with mosquito repellents which alter the mosquitos' host seeking behaviour. We perform a viability analysis of the model, which amounts to finding a viability kernel, or a set of initial conditions such that the proportion of infected individuals in the controlled system remains below a target infection cap for all future times. The viability kernel is characterised by a variational formulation. It is computed numerically from the sub-zero level-set of a value function that solves a Hamilton-Jacobi-Bellman equation.