Analyzing the Dynamics of a Rumor Transmission Model with Incubation. (22nd April 2012)

• Record Type: Journal Article
• Authors: Huo, Liang'an; Huang, Peiqing; Guo, Chun-xiang
• Other Names: El-Morshedy Hassan A. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-04-22
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/328151
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : This paper considers a rumor transmission model with incubation that incorporates constant recruitment and has infectious force in the latent period and infected period. By carrying out a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we use the geometric approach for ordinary differential equations which is based on the use of higher-order generalization of Bendixson's criterion. It shows that either the number of rumor infective individuals tends to zero as time evolves or the rumor persists. We prove that the transcritical bifurcation occurs atR 0 crosses the bifurcation thresholdR 0 = 1 by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function ofR 0, as a consequence for successful eradication of the rumor, one should simply reduceR 0 continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.