  The study of epidemiological systems has generated deep interest in exploring
the dynamical complexity of common infectious diseases driven by seasonally
varying contact rates. Mathematical modeling and field observations have shown
that, under seasonal variation, the incidence rates of some endemic infectious
diseases fluctuate dramatically and the dynamics is often characterized by
chaotic oscillations in the absence of specific vaccination programs. In fact,
the existence of chaotic behavior has been precisely stated in the literature
as a noticeable feature in the dynamics of the classical
Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However,
in the context of epidemiology, chaos is often regarded as an undesirable
phenomenon associated with the unpredictability of infectious diseases. As a
consequence, the problem of converting chaotic motions into regular motions
becomes particularly relevant. In this article, we consider the phase control
technique applied to the seasonally forced SIR epidemic model to suppress
chaos. Interestingly, this method of controlling chaos takes on a clear meaning
as a weak perturbation on a seasonal vaccination strategy. Numerical
simulations show that the phase difference between the two periodic forces -
contact rate and vaccination - plays a very important role in controlling
chaos.
