Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 328151, 21 pages
Research Article

Analyzing the Dynamics of a Rumor Transmission Model with Incubation

1Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China
2Business School of Sichuan University, Chengdu 610065, China

Received 9 November 2011; Accepted 3 January 2012

Academic Editor: Hassan A. El-Morshedy

Copyright © 2012 Liang'an Huo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 at R0 crosses the bifurcation threshold R0=1 by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function of R0, as a consequence for successful eradication of the rumor, one should simply reduce R0 continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.