Periodic solutions and bifurcation in an epidemic model with birth pulses

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.