Analysis on a delayed SIRS epidemic model with impulsive vaccination

摘要

An SIRS model with discrete delay, pulse vaccination and non-monotonic incidence is studied.We gave two new threshold values R1 and R2. Further, using the comparison theorem of impulsivedifferential equation and Lyapunov functional, we proved that, under the condition R1＜1, the disease-freeperiodic solution is globally attractive, and that R2＞1 implies permanence of the disease. For R1＞1＞R2,numerical simulation illustrates that the disease will be permanent.