Bull Math Biol. 2013 Oct;75(10):1716-46. doi: 10.1007/s11538-013-9866-x.
W.O. Kermack and A.G. McKendrick introduced in their fundamental paper, A Contribution to the Mathematical Theory of Epidemics, published in 1927, a deterministic model that captured the qualitative dynamic behavior of single infectious disease outbreaks. A Kermack–McKendrick discrete-time general framework, motivated by the emergence of a multitude of models used to forecast the dynamics of epidemics, is introduced in this manuscript. Results that allow us to measure quantitatively the role of classical and general distributions on disease dynamics are presented. The case of the geometric distribution is used to evaluate the impact of waiting-time distributions on epidemiological processes or public health interventions. In short, the geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship involving the control reproduction number, a function of transmission parameters and the means of distributions used to model disease or intervention control measures, is computed. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions. Examples, using the geometric, Poisson and binomial distributions, are used to highlight the impact of the choices made in quantifying the risk posed by single outbreaks and the relative importance of various control measures.
W.O. Kermack 和 A.G. McKendrick 在他们 1927 年发表的开创性论文《传染病数学理论的贡献》中提出了一个确定性模型，该模型捕捉了单一传染病爆发的定性动态行为。本文引入了一个受多种用于预测传染病动力学模型出现的启发的 Kermack-McKendrick 离散时间通用框架。提出了一些结果，这些结果使我们能够定量衡量经典和一般分布对疾病动态的作用。利用几何分布的情况来评估等待时间分布对流行病学过程或公共卫生干预的影响。简而言之，使用几何分布来建立基本或零流行病学模型，以检验实际阶段期分布对单一传染病爆发动态的相关性。计算了一个涉及控制繁殖数的最终大小关系，该控制繁殖数是传输参数和用于对疾病或干预控制措施建模的分布均值的函数。模型结果和模拟突出了使用特定参数分布进行预测时出现的不一致性。使用几何分布、泊松分布和二项式分布的示例，突出了量化单个爆发风险的选择以及各种控制措施的相对重要性所带来的影响。
