COMPLEXITY AND ASYMPTOTICAL BEHAVIOR OF A SIRS EPIDEMIC MODEL WITH PROPORTIONAL IMPULSIVE VACCINATION

This paper considers an SIRS epidemic model with proportional impulsive vaccination, which may inherently oscillate. We study the ratio-dependent impulsive control and obtain the conditions about the basic reproductive number for which the epidemic-elimination solution is globally asymptotic. On the other hand, if the epidemic turns out to be endemic, we study numerically the influences of impulsive vaccination on the periodic oscillation of a system without impulsion and find sophisticated phenomena such as chaos in this case.