Abstract：
The overall course of the COVID-19 pandemic in Western countries has been characterized by complex sequences of phases. In the period before the arrival of vaccines, these phases were mainly due to the alternation between the strengthening/lifting of social distancing measures, with the aim to balance the protection of health and that of the society as a whole. After the arrival of vaccines, this multi-phasic character was further emphasized by the complicated deployment of vaccination campaigns and the onset of virus\' variants. To cope with this multi-phasic character, we propose a theoretical approach to the modeling of overall pandemic courses, that we term multi-period/multi-phasic, based on a specific definition of phase. This allows a unified and parsimonious representation of complex epidemic courses even when vaccination and virus\' variants are considered, through sequences of weak ergodic renewal equations that become fully ergodic when appropriate conditions are met. Specific hypotheses on epidemiological and intervention parameters allow reduction to simple models. The framework suggest a simple, theory driven, approach to data explanation that allows an accurate reproduction of the overall course of the COVID-19 epidemic in Italy since its beginning (February 2020) up to omicron onset, confirming the validity of the concept.
摘要：
西方国家COVID-19大流行的总体过程具有复杂的阶段序列。在疫苗到来之前，这些阶段主要是由于加强/解除社会距离措施之间的交替，旨在平衡对健康和整个社会的保护。疫苗到达后，疫苗接种活动的复杂部署和病毒变种的发作进一步强调了这种多阶段特征.为了应对这种多相特征，我们提出了一种理论方法来建模整个大流行课程，我们称之为多周期/多阶段，基于阶段的具体定义。即使考虑到疫苗接种和病毒变种，这也可以统一和简约地表示复杂的流行病过程。通过在满足适当条件时变得完全遍历的弱遍历更新方程序列。关于流行病学和干预参数的特定假设可以简化为简单的模型。该框架提出了一个简单的，理论驱动，数据解释的方法，可以准确再现意大利自COVID-19疫情开始(2020年2月)到omicron发病的总体过程，确认概念的有效性。
