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Y. N. Kyrychko and K. B. Nlyuss, “Global Properties of a Delayed SIR Model with Temporary Immunity and Nonlinear Incidence Rate,” Nonlinear Analysis: Real World Applications, Vol. 6, No. 3, 2005, pp. 495-507. doi:10.1016/j.nonrwa.2004.10.001

has been cited by the following article:

• TITLE: Stability of a Delayed SIQRS Model with Temporary Immunity

  AUTHORS: Laid Chahrazed, Rahmani Fouad Lazhar

  KEYWORDS: Adomian Method; Epidemiology; Mathematical Model; The Epidemic Model; The Equilibrium Points

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.2, March 5, 2013

  ABSTRACT: This paper addresses a time-delayed SIQRS model with a linear incidence rate. Immunity gained by experiencing the disease is temporary; whenever infected, the disease individuals will return to the susceptible class after a fixed period of time. First, the local and global stabilities of the infection-free equilibrium are analyzed, respectively. Second, the endemic equilibrium is formulated in terms of the incidence rate, and locally asymptotic stability. Finally we use the adomian decomposition method is applied to the system epidemiologic. This method yields an analytical solution in terms of convergent infinite power series.