Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment. (19th July 2012)

• Record Type: Journal Article
• Authors: Xue, Yakui; Wang, Junfeng
• Other Names: Zizovic Malisa R. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-07-19
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/647853
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.