ABSTRACT In this paper, an impulsive epidemic model with time delay is proposed, which susceptible population is divided into two groups: high risk susceptibles and non-high risk susceptibles. We introduce two thresholds R1, R2 and demonstrate that the disease will be extinct if R1<1 and persistent if R2 >1 . Our results show that larger pulse vaccination rates or a shorter the period of pulsing will lead to the eradication of the disease. The conclusions are confirmed by numerical simulations.
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