A well-known characteristic of recent pandemics is the high level of heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify the effects of this phenomenon, we analyze the effect of the variance and higher moments of the infection distribution on the spread of the disease. Working in the framework of stochastic branching processes, we derive an approximate analytical formula for the probability of avoiding an outbreak in the high variance regime of the infection distribution, verify it numerically and analyze its regime of validity in various examples. We perform population based simulations and show that, as predicted by the mathematical model, it is possible for an outbreak not to occur in the high variance regime even when the basic reproduction number R ₀ is larger than 1. The applicability of our results to the current COVID-19 is restricted to scenarios where imposed measures are able to reduce significantly the number of infected individuals and the high basic reproduction number. We note that our analysis may find implications in general information spread scenarios.

近期大流行的一个众所周知的特征是感染传播的高度异质性：并非所有受感染的个体都以相同的速度传播疾病，而某些个体（超级传播者）是造成大部分感染的罪魁祸首。为了量化这种现象的影响，我们分析了感染分布的方差和较高矩对疾病传播的影响。在随机分支过程的框架内，我们推导出了在感染分布的高方差范围内避免爆发的概率的近似分析公式，对其进行数值验证并在各种示例中分析其有效性范围。我们执行基于人口的模拟并表明，正如数学模型所预测的那样，R ₀大于 1。我们的结果对当前 COVID-19 的适用性仅限于采取措施能够显着减少受感染个体数量和高基本繁殖数量的情况。我们注意到，我们的分析可能会在一般信息传播场景中找到影响。