Epidemiological models with the identical basic reproduction number ${\mathcal{R}}_0$ may behave differently on both short time scale and long time scale. In this paper, we compare the predicted final sizes for several deterministic epidemic models and estimate the probabilities of a minor/major outbreak for continuous-time Markov chain (CTMC) models, all epidemic models have the identical ${\mathcal{R}}_0$. It is proved that the final size predicted by the epidemic model with homogeneous mixing is larger than with heterogeneous mixing. For CTMC models with heterogeneous mixing, the probabilities of a minor outbreak initiated by superspreaders and non-superspreaders are calculated and compared. For both deterministic modelling and stochastic modelling, numerical simulations are performed to support the mathematical analysis.

具有相同基本再生数的流行病学模型 ${\mathcal{电阻}}_0$可能在短时间尺度和长时间尺度上表现不同。在本文中，我们比较了几种确定性流行病模型的预测最终大小，并估计了连续时间马尔可夫链 (CTMC) 模型的小/大爆发的概率，所有流行病模型都具有相同的${\mathcal{电阻}}_0$. 证明了均匀混合的流行病模型预测的最终大小大于非均匀混合的流行模型。对于具有异构混合的 CTMC 模型，计算和比较由超级传播者和非超级传播者发起的小爆发的概率。对于确定性建模和随机建模，执行数值模拟以支持数学分析。