Hernandez-Ceron Nancy, Chavez-Casillas Jonathan A, Feng Zhilan
Purdue University, West Lafayette, IN 47907, United States.
Math Biosci. 2015 Mar;261:74-82. doi: 10.1016/j.mbs.2014.12.003. Epub 2014 Dec 27.
In this study, a stochastic discrete-time model is developed to study the spread of an infectious disease in an n-patch environment. The model includes an arbitrary distribution of the (random) infectious period T, and the results are used to investigate how the distribution of T may influence the model outcomes. General results are applied to specific distributions including Geometric, Negative Binomial, Poisson and Uniform. The model outcomes are contrasted both numerically and analytically by comparing the corresponding basic reproduction numbers R0 and probability of a minor epidemic (or probability of disease extinction) P0. It is shown analytically that for n = 2 the reproduction numbers corresponding to different distributions of T can be ordered based on the probability generating function ϕT of T. In addition, numerical simulations are carried out to examine the final epidemic size F and duration of the epidemic D of a two-patch model.
在本研究中，开发了一个随机离散时间模型来研究传染病在n斑块环境中的传播。该模型包括（随机）感染期T的任意分布，并利用结果研究T的分布如何影响模型结果。一般结果应用于包括几何分布、负二项分布、泊松分布和均匀分布在内的特定分布。通过比较相应的基本再生数R0和小规模疫情的概率（或疾病灭绝的概率）P0，对模型结果进行了数值和分析对比。分析表明，对于n = 2，对应于T不同分布的再生数可以基于T的概率生成函数ϕT进行排序。此外，还进行了数值模拟，以检验双斑块模型的最终疫情规模F和疫情持续时间D。
