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In mathematical epidemiology, epidemic control often aims at driving thenumber of infected individuals to zero, asymptotically. However , during thetransitory phase, the number of infected can peak at high values. In thispaper, we consider mosquito vector control in the Ross-Macdonaldepidemiological model, with the goal of capping the proportion of infected bydengue at the peak. We formulate this problem as one of control of a dynamicalsystem under state constraint. We allow for time-dependent fumigation rates toreduce the population of mosquito vector, in order to maintain the proportionof infected individuals by dengue below a threshold for all times. Theso-called viability kernel is the set of initial states (mosquitoes andinfected individuals) for which such a fumigation control trajectory exists.Depending on whether the cap on the proportion of infected is low, high ormedium, we provide different expressions of the viability kernel. We alsocharacterize so-called viable policies that produce, at each time, a fumigationrate as a function of current proportions of infected humans and mosquitoes,such that the proportion of infected humans remains below a threshold for alltimes. We provide a numerical application in the case of control of a dengueoutbreak in 2013 in Cali, Colombia.

Viable Control of an Epidemiological Model