Abstract：Early warning signals (EWS) from the theory of critical slowing down can anticipate the threshold of disease elimination process and provide scientific guidance for disease elimination plans. In this paper, we consider the SIR stochastic model with multiple simulations for incidence data and calculate the area under the curve to evaluate the effect of EWS behaviors. We find that EWS remains effective even at high initial levels of immunity, although its effectiveness diminishes compared to scenarios where the initial immunity rate is zero. Mean and variance are sensitive to the system with a decrease in the number of cases, while the coefficient of variation is not only robust but also exhibits excellent discriminatory effects as the system approaches or moves away from the tipping point. Autocovariance, lag-1 autocorrelation and decay time increase before the system approach to the tipping point.
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