Internal eradicability of a diffusive epidemic system via feedback control

This paper concerns a two-component reaction–diffusion system modeling an (SI) epidemic system. The possibility of eradicating the epidemic, acting on the infected population in a subregion ωω, is related to the magnitude of the principal eigenvalue to a certain elliptic operator. We obtain some results and remarks concerning the evaluation of this principal eigenvalue in connection with the geometry of the domain and of the support of the control. The problem of finding the position of the support of a stabilizing feedback control with a very simple structure, which provides a fast eradication of the epidemic is also investigated. A conceptual iterative algorithm to decrease at each iteration the size of the infected population at a moment TT, by translating ωω, is derived.