We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of basic reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.
翻译:我们提出一种随机流行病模式,以研究各种预防措施,如统一减少接触和传染、接种疫苗、隔离、筛查和接触追踪等,对同一混合社区疾病爆发的影响;该模式以感染过程为基础,我们通过随机接触和传染过程确定这种过程,以便每个人有独立的感染特征;特别是,我们监测繁殖次数和一代时间分布的变化情况;我们表明,一些干预措施,即统一减少和接种,影响前者,而后一措施则保持不变,而其他干预措施,即隔离、筛查和接触追踪,则影响这两个数量;我们对这些数量的变化进行理论分析,我们表明,在实际中,一代时间分布的变化可能很大,在估计基本生殖数字时可能造成偏差;框架由于其一般性质,可以捕捉许多传染病的特性,但特别强调COVID-19,对此提供了数字结果。