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Dynamics of infectious diseases and pulse vaccination: Teasing apart the embedded resonance effects. (English) Zbl 1110.34031
Summary: Dynamical systems theory predicts that inherently oscillatory systems undergoing periodic forcings will exhibit resonance phenomena, which are characterized by qualitative dynamical consequences resulting from the amplification of small external perturbations. In this paper, we use extensive numerical simulations to demonstrate that the periodic nature of pulse vaccination strategies can make disease dynamics resonate. We proceed step by step in order to tease apart the dynamical consequences of (i) the intrinsic nonlinearity of the host-pathogen system, (ii) the seasonal variation in transmission and (iii) the additional forcing caused by vaccinating in pulses. We document that the resonance phenomenon associated with pulse vaccination can have quantitative epidemiological implications and produce perverse effects such as an unexpected increase in the number of infectives as the vaccination frequency increases. Our findings emphasize the importance of carefully taking into account the dynamical properties of the disease when designing a pulse vaccination strategy.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
34D05Asymptotic stability of ODE
34C25Periodic solutions of ODE
92D30Epidemiology