Dynamics of infectious diseases and pulse vaccination: Teasing apart the embedded resonances effects

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.