Infectious diseases on farms pose both public and animal health risks, so understanding how they spread between farms is crucial for developing disease control strategies to prevent future outbreaks. We develop novel Bayesian nonparametric methodology to fit spatial stochastic transmission models in which the infection rate between any two farms is a function that depends on the distance between them, but without assuming a specified parametric form. Making nonparametric inference in this context is challenging since the likelihood function of the observed data is intractable because the underlying transmission process is unobserved. We adopt a fully Bayesian approach by assigning a transformed Gaussian process prior distribution to the infection rate function, and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to perform Bayesian inference. We use the posterior predictive distribution to simulate the effect of different disease control methods and their economic impact. We analyse a large outbreak of avian influenza in the Netherlands and infer the between-farm infection rate, as well as the unknown infection status of farms which were pre-emptively culled. We use our results to analyse ring-culling strategies, and conclude that although effective, ring-culling has limited impact in high-density areas.

中文翻译：

---

2003 年荷兰高致病性禽流感暴发的贝叶斯非参数分析

农场的传染病对公共和动物健康构成威胁，因此了解它们如何在农场之间传播对于制定疾病控制策略以防止未来爆发至关重要。我们开发了新的贝叶斯非参数方法来拟合空间随机传播模型，其中任意两个农场之间的感染率是一个取决于它们之间距离的函数，但不假设特​​定的参数形式。在这种情况下进行非参数推理具有挑战性，因为观察到的数据的似然函数是难以处理的，因为潜在的传输过程是未观察到的。我们采用完全贝叶斯方法，通过将转换后的高斯过程先验分布分配给感染率函数，然后开发一种有效的数据增强马尔可夫链蒙特卡罗算法来执行贝叶斯推理。我们使用后验预测分布来模拟不同疾病控制方法的效果及其经济影响。我们分析了荷兰的一次禽流感大爆发，并推断出农场之间的感染率，以及被先发制人地扑杀的农场的未知感染状态。我们使用我们的结果来分析环形剔除策略，并得出结论，尽管有效，但环形剔除在高密度区域的影响有限。以及被先发制人扑杀的农场的未知感染状态。我们使用我们的结果来分析环形剔除策略，并得出结论，尽管有效，但环形剔除在高密度区域的影响有限。以及被先发制人扑杀的农场的未知感染状态。我们使用我们的结果来分析环形剔除策略，并得出结论，尽管有效，但环形剔除在高密度区域的影响有限。