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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 354287, 11 pages
http://dx.doi.org/10.1155/2013/354287
Research Article

Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates

1School of Science, Department of Fundamental Mathematics, Jiamusi University, Jiamusi 154007, China
2School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 26 January 2013; Revised 16 June 2013; Accepted 22 July 2013

Academic Editor: Pagavathi Balasubramaniam

Copyright © 2013 Ling Zhang 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.

Abstract

We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production number . The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.