Regional Control for a Class of Spatially Structured Epidemics: Think Globally, Act Locally

This chapter introduces the problem of controlling a paradigmatic spatially structured epidemic system modelled as an integro-differential reaction–diffusion system. The spread of the epidemic is due to the interaction of the relevant population (humans, animals, trees, etc.) with a polluted environment. The public health concern consists of reducing the disease in the relevant habitat, as fast as possible, at an optimal cost. The underlying issue of our presentation is that very often the entire domain of interest for the epidemic is either unknown or difficult to manage, for an affordable implementation of suitable environmental sanitation programs. This is the reason why regional control has been proposed; it has been shown that, under suitable modelling assumptions, it is indeed sufficient to implement such programs only in a given subregion, conveniently chosen, so to lead to an effective reduction, and eventual eradication, of the epidemic in the whole habitat; it is evident that this practice may have an enormous importance in real cases with respect to both financial and practical affordability.