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Dynamic complexities in a seasonal prevention epidemic model with birth pulses. (English) Zbl 1064.92039

Summary: 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. We propose an epidemic model with density-dependent birth pulses and seasonal prevention. Using a discrete dynamical system determined by a stroboscopic map, we obtain 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.

MSC:

92D30 Epidemiology
92D25 Population dynamics (general)
34D23 Global stability of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
37N25 Dynamical systems in biology
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