On the dynamics of a delayed SIR epidemic model with a modified saturated incidence rate. (English) Zbl 1183.37092

Kaddar, Abdelilah

Electron. J. Differ. Equ. 2009, Paper No. 133, 7 p. (2009).

The author has suggested a delayed susceptible-infective-removed (SIR) epidemic model with a modified saturated incidence rate, which consists of three rationally dependent three ODEs. The first two equations of this system do not depend on the third equation, that can be omitted without loss of generality. The dynamics of the obtained system is studied in terms of local stability and of the description of the Andronov-Hopf bifurcation, that is proven to exist as the delay \(\tau\) in time cross some critical value. Numerical illustrating example is given to confirm the theoretical analysis.

Reviewer: Irina V. Konopleva (Ul’yanovsk)

MSC:

37G15	Bifurcations of limit cycles and periodic orbits in dynamical systems
92D30	Epidemiology

Keywords:

susceptible-infective-removed (SIR) epidemic model; incidence rate; delayed differential equations; Hopf bifurcation; periodic solutions