A central feature of pandemics is the emergence and decay of localized infection waves. While traditional SIR models for infectious diseases can reproduce such waves, they fail to capture two key features. First, SIR models are unable to represent short-duration super-spreader events which often trigger infection waves in a community. Second, SIR models predict exponential decay to an asymptotic state after the infection wave peaks. In contrast, observations suggest a slower algebraic decay. In this paper, we develop models for the basic reproduction number $R_0$ to capture these features. To generate quantitative estimates for $R_0$ during super-spreader events, we reconcile the SIR framework with the Wells–Riley model for airborne disease transmission. We also show that algebraic decay emerges naturally if models are modified to account for the behavioral tendency towards relaxing precautions as the infected fraction decreases. This approach merges for the first time behavioral with physicochemical aspects.

大流行的一个核心特征是局部感染波的出现和衰减。虽然传统的传染病 SIR 模型可以重现这种波，但它们未能捕捉到两个关键特征。首先，SIR 模型无法表示经常在社区中引发感染波的短期超级传播者事件。其次，SIR 模型预测感染波达到峰值后指数衰减到渐近状态。相反，观察表明代数衰减较慢。在本文中，我们开发了基本再生数的模型$R_0$捕捉这些特征。生成定量估计$R_0$在超级传播者事件期间，我们将 SIR 框架与用于空气传播疾病传播的 Wells-Riley 模型进行了协调。我们还表明，如果修改模型以解释随着感染比例减少而放松预防措施的行为趋势，代数衰减自然会出现。这种方法首次将行为与物理化学方面相结合。