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H. Wei, X. Li and M. Martcheva, “An Epidemic Model of a Vector-Borne Disease with Direct Transmission and Time Delay,” Journal of Mathematical Analysis and Applications, Vol. 342, No. 2, 2008, pp. 895-908. http://dx.doi.org/10.1016/j.jmaa.2007.12.058

has been cited by the following article:

• TITLE: Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

  AUTHORS: Wanwan Wang, Maoxing Liu, Jinqing Zhao

  KEYWORDS: Exponential Birth; SIR Model; Time Delay; Hurwitz Criterion; Hopf Bifurcation

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10B, October 4, 2013

  ABSTRACT: In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay; and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriatecritical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.