Abstract
In this paper, we proposed and analyzed a new stochastic SIRVI epidemic model considering weak immunity generated after vaccination. The dynamics of the model is studied under white noise disturbance. We proved that the disease will eventually disappear if R1s<1, and the disease is persistent if R2s>1. Moreover, we found that the appearance of stochastic environmental disturbance can affect the transmission of infectious diseases, and relatively high noise intensity can suppress the spread of diseases under certain conditions.
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