Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to complex stochastic models. Such complexity together with data characteristics make the analysis of these systems a challenge. Our objective was to develop a new inference procedure to estimate key parameters of stochastic metapopulation models of animal disease spread from longitudinal and spatial datasets, while accurately accounting for characteristics of census data. We applied our procedure to provide new knowledge on the regional spread of \emph{Mycobacterium avium} subsp. \emph{paratuberculosis} (\emph{Map}), which causes bovine paratuberculosis, a worldwide endemic disease. \emph{Map} spread between herds through trade movements was modeled with a stochastic mechanistic model. Comprehensive data from 2005 to 2013 on cattle movements in 12,857 dairy herds in Brittany (western France) and partial data on animal infection status in 2,278 herds sampled from 2007 to 2013 were used. Inference was performed using a new criterion based on a Monte-Carlo approximation of a composite likelihood, coupled to a numerical optimization algorithm (Nelder-Mead Simplex-like). Our criterion showed a clear superiority to alternative ones in identifying the right parameter values, as assessed by an empirical identifiability on simulated data. Point estimates and profile likelihoods allowed us to establish the initial state of the system, identify the risk of pathogen introduction from outside the metapopulation, and confirm the assumption of the low sensitivity of the diagnostic test. Our inference procedure could easily be applied to other spatio-temporal infection dynamics, especially when ABC-like methods face challenges in defining relevant summary statistics.

翻译：时空病原体传播通常在荟萃种群尺度下部分可观测。现有数据多为代理变量，存在不完整、删失及异质性特征。此外，此类生物系统的建模往往涉及复杂随机模型，这种复杂性结合数据特征使得系统分析极具挑战。本研究旨在开发一种新的推断方法，利用纵向与空间数据集估计动物疾病传播随机荟萃种群模型的关键参数，同时准确反映普查数据特征。我们应用该方法为牛副结核病（一种全球性地方性流行病）的致病菌——鸟分枝杆菌副结核亚种（Mycobacterium avium subsp. paratuberculosis, Map）的区域传播提供新见解。采用随机机制模型对通过贸易流动的Map在牛群间传播进行建模，使用2005-2013年法国布列塔尼地区12,857个奶牛群的完整牛只流动数据，以及2007-2013年2,278个抽样牛群的动物感染状态部分数据。基于复合似然的蒙特卡洛近似准则，结合数值优化算法（类Nelder-Mead单纯形法）进行推断。经模拟数据经验可识别性评估，本研究准则在识别正确参数值方面显著优于替代方法。通过点估计与轮廓似然，我们确定了系统初始状态，识别了外部病原体引入荟萃种群的风险，并验证了诊断检测低敏感性的假设。本推断方法可便捷应用于其他时空感染动态研究，尤其适用于类ABC方法难以定义有效汇总统计量的场景。