Modelling epidemics is crucial for understanding the emergence, transmission, impact and control of diseases. Spatial individual-level models (ILMs) that account for population heterogeneity are a useful tool, accounting for factors such as location, vaccination status and genetic information. Parametric forms for spatial risk functions, or kernels, are often used, but rely on strong assumptions about underlying transmission mechanisms. Here, we propose a class of non-parametric spatial disease transmission model, fitted within a Bayesian Markov chain Monte Carlo (MCMC) framework, allowing for more flexible assumptions when estimating the effect on spatial distance and infection risk. We focus upon two specific forms of non-parametric spatial infection kernel: piecewise constant and piecewise linear. Although these are relatively simple forms, we find them effective. The performance of these models is examined using simulated data, including under circumstances of model misspecification, and then applied to data from the UK 2001 foot-and-mouth disease.

翻译：建模流行病对于理解疾病的出现、传播、影响及控制至关重要。考虑人群异质性的空间个体水平模型（ILMs）是一种有用工具，可纳入位置、疫苗接种状态和遗传信息等因素。空间风险函数（或核函数）常采用参数形式，但这些形式依赖于对潜在传播机制的强假设。本文提出一类非参数空间疾病传播模型，基于贝叶斯马尔可夫链蒙特卡洛（MCMC）框架拟合，在估计空间距离与感染风险影响时允许更灵活的假设。我们重点研究两种特定形式的非参数空间感染核：分段常数型和分段线性型。尽管这些形式相对简单，但发现其效果良好。通过模拟数据（包括模型设定错误的情况）检验这些模型的性能，并将其应用于英国2001年口蹄疫疫情数据。