Containment strategies of epidemic invasions

In this paper, prompted by the practical issue of controlling the Aujeszky disease affecting hogs, we analyse what strategies can be implemented to try and contain an SI epidemic invasion in one and two neighbouring farms. We perform some simulations under different assumptions on the basic system, leading thus to different models. The results show that the disease cannot be arrested completely, since infected remain so for life and the system is of a diffusive type, but its spread can rather be slowed down. The influence of contamination islands, sudden external disease infiltration and containment barriers are simulated. The possible leaking of the infection into a neighbouring farm is also studied. The analysis is then extended to an SIS model allowing disease recovery. Under suitable conditions, harvesting is shown to be an effective containment strategy.