  Managing infectious diseases is a world public health issue, plagued by
uncertainties. In this paper, we analyze the problem of viable control of a
dengue outbreak under uncertainty. For this purpose, we develop a controlled
Ross-Macdonald model in discrete time, with mosquito vector control by
fumigation and with uncertainties affecting the dynamics. The robust viability
kernel is the set of all initial states such that there exists at least a
strategy of insecticide spraying which guarantees that the number of infected
people remains below a threshold, for all times, and whatever the sequences of
uncertainties (scenarios). Having chosen three nested subsets of uncertainties
- a deterministic one (without uncertainty), a medium one and a large one - we
can measure the incidence of the uncertainties on the size of the kernel, in
particular on its reduction with respect to the de-terministic case. The
numerical results show that the viability kernel without uncertainties is
highly sensitive to the variability of parameters - here the biting rate, the
probability of infection to mosquitoes and humans, and the proportion of female
mosquitoes per person. So the robust viability kernel is a possible tool to
reveal the importance of uncertainties regarding epidemics control.
