Optimal Control of an Epidemic through Educational Campaigns

In this work we study the best strategy for educational campaigns during the outbreak of an epidemic. Assuming that the epidemic is described by the simplified SIR model and that the total time of the campaign is limited due to budget, we consider two possible scenarios. In the first scenario we have a campaign oriented to decrease the infection rate by stimulating susceptibles to have a protective behavior. In the second scenario we have a campaign oriented to increase the removal rate by stimulating the infected to remove themselves from the infected class. The optimality is taken to be to minimize the total number of infected by the end of the epidemic outbreak. The technical tool used to determine the optimal strategy is the Pontryagin Maximum Principle.