Trapman Pieter, Meester Ronald, Heesterbeek Hans
Faculty of Veterinary Medicine, Utrecht University, Yalelaan 7, 3584 Utrecht CL, The Netherlands.
J Math Biol. 2004 Dec;49(6):553-76. doi: 10.1007/s00285-004-0267-5. Epub 2004 Mar 3.
This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environment. With this branching process, we estimate the probability of extinction and the expected number of infected individuals for different control measures. We also use this branching process to calculate the generating function of the number of infected individuals at any given moment. The model and methods are designed using important infections of farmed animals, such as classical swine fever, foot-and-mouth disease and avian influenza as motivating examples, but have a wider application, for example to emerging human infections that lead to strict quarantine of cases and suspected cases (e.g. SARS) and contact and movement restrictions.
本文关注的是一个随机模型，该模型描述了可能对动物或人类健康造成重大影响的传染病爆发情况，并且可能导致严重的经济损失，因此需要立即采取一系列措施来遏制其传播。在这类疾病的爆发过程中，由于后续采取的控制措施，病原体所处的环境会发生变化。在我们的模型中，我们引入了一个在变化（但非随机）环境中的一般分支过程。通过这个分支过程，我们估计不同控制措施下的灭绝概率和受感染个体的预期数量。我们还使用这个分支过程来计算在任何给定时刻受感染个体数量的生成函数。该模型和方法以养殖动物的重要传染病，如经典猪瘟、口蹄疫和禽流感为示例进行设计，但具有更广泛的应用，例如适用于导致对病例和疑似病例进行严格隔离（如非典）以及限制接触和流动的新型人类感染疾病。
