Periodic solutions and bifurcation in an [Formula: see text] epidemic model with birth pulses

Guirong Jiang; Qigui Yang

doi:10.1016/j.mcm.2009.04.021

Periodic solutions and bifurcation in an $S I S$ epidemic model with birth pulses

Math Comput Model. 2009 Aug;50(3):498-508. doi: 10.1016/j.mcm.2009.04.021. Epub 2009 May 30.

Authors

Guirong Jiang^{1

2}, Qigui Yang²

Affiliations

¹ School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China.
² School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China.

Abstract

The dynamical behavior of an $S I S$ epidemic model with birth pulses and a varying population is discussed analytically and numerically. This paper investigates the existence and stability of the infection-free periodic solution and the endemic periodic solution. By using discrete maps, the center manifold theorem, and the bifurcation theorem, the conditions of existence for bifurcation of the positive periodic solution are derived. Moreover, numerical results for phase portraits, periodic solutions, and bifurcation diagrams, which are illustrated with an example, are in good agreement with the theoretical analysis.

Keywords: S I S epidemic model; Flip bifurcation; Periodic solution; Pulse birth.