title: Media alert in an SIS epidemic model with logistic growth.
abstract: 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 an 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.
authors.affiliation: a School of Mathematics and Statistics , Central China Normal University , Wuhan , People's Republic of China.
authors.forename: Lianwen
authors.initials: L
authors.lastname: Wang
authors.affiliation: b School of Mathematical Sciences , Xiamen University , Xiamen , People's Republic of China.
authors.forename: Da
authors.initials: D
authors.lastname: Zhou
authors.affiliation: c Department of Mathematics , Hubei University for Nationalities , Hubei , People's Republic of China.
authors.forename: Zhijun
authors.initials: Z
authors.lastname: Liu
authors.affiliation: c Department of Mathematics , Hubei University for Nationalities , Hubei , People's Republic of China.|d Department of Mathematics , Southern Illinois University , Carbondale , IL , USA.
authors.forename: Dashun
authors.initials: D
authors.lastname: Xu
authors.affiliation: a School of Mathematics and Statistics , Central China Normal University , Wuhan , People's Republic of China.
authors.forename: Xinan
authors.initials: X
authors.lastname: Zhang
mesh_terms: D003141:Communicable Diseases / Q000635:transmission*; D003146:Communications Media; D058872:Epidemics; D006801:Humans; D008954:Models, Biological
keywords: 34K18; 34K20; 92D30; SIS epidemic model; bi-stability; logistic growth; media alert; multiple endemic equilibria