| Abstract: |
| This study develops stochastic difference equation models to characterize COVID-19 transmission dynamics under random effects. First, we establish a discrete-time stochastic epidemic model using binomial distributions, with parameters estimated from reported data. Next, we construct an improved model that incorporates asymptomatic transmission and imported cases to quantify resurgence risk and evaluate containment measures. An analysis of over 100 Chinese outbreaks reveals small-scale clustered transmission patterns under non-pharmaceutical interventions (NPIs). To investigate how stochastic factors influence the containment process, we derive a stochastic difference equation for newly reported cases based on the stochastic SIR framework and introduce the Stochastic Control Reproduction Number (SCRN). We further estimate the SCRN through Bayesian change-point analysis, and demonstrate via first-passage time theory that controlled randomness can accelerate epidemic containment. |
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