In   general, media coverage would not be implemented unless the number of   infected cases reaches some critical number. To reflect this feature, we   incorporate the media effect and a critical number of infected cases into the   disease transmission rate and consider a susceptible-infected-susceptible   epidemic model with logistic growth. Our model analysis shows that early   media alert and strong media effects are preferable to decrease the numbers   of infected cases at endemic equilibria. Furthermore, we noticed that the   model may have up to three endemic equilibria and bi-stability can occur in a   threshold interval for the critical number. Note that the interval depends on   parameters for the focal disease and the media effect. It is possible to   roughly estimate the interval for re-emerging diseases in a given region.   Therefore, the result could be useful to health policymakers. Global   stability is also obtained when the model admits a unique endemic   equilibrium.