Dynamic complexities in a seasonal prevention epidemic model with birth pulses

In most of population dynamics, increases in population due to birth are assumed to be time-dependent, but many species reproduce only during a single period of the year. In this paper, we propose an epidemic model with density-dependent birth pulses and seasonal prevention. Using the discrete dynamical system determined by stroboscopic map, we obtain the local or global stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the epidemic model with birth pulses and seasonal prevention are very complex, including small amplitude oscillations, large-amplitude multi-annual cycles and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that may lead a period-doubling route to chaos.