Suppose new infectives appear regularly, so that t k+1t k = τ. (If not, the analysis generalizes quite easily.) For t k <t <t k+1 , we have It follows that the endemic equilibrium is stable if Î >I crit . Thus, even in an extremely simplified version of the model, the media may make things significantly worse than if no media effect were included. We kept this model deliberately simple, partly for mathematical tractability and partly to show that the media effects apply even in this idealised scenario.