I consider a simple model for a vector-borne disease with control intervention subject to constraints on the control input and on the phase variable representing the size of the infected human compartment. The task is to determine the viability kernel associated to the constraints, or equivalently, the set of those initial states for which solutions of the model respect these constraints for all future times.

Using results from classical dynamical systems, it is possible to tell when the viability kernel has either positive or zero Lebesgue measure in the phase space. Furthermore, this set can also be approximated numerically following a variational approach, whereby the sub-zero level set of a value function, solving an appropriate equation of Hamilton-Jacobi-Bellman type, defines the kernel.

I will present an analysis of viability for two models for vector-borne disease with compartmental structure: Susceptible-Infected for the mosquito vector, and a) Susceptible-Infected-Susceptible; and b) Susceptible-Infected-Recovered for the human host.