Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, Olshausenstr. 40, D-24098, Kiel, Germany; Unit for Biomathematics and Data Processing, Faculty of Veterinary Medicine, Justus Liebig University, Frankfurter Str. 95, D-35392, Giessen, Germany.
Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, Olshausenstr. 40, D-24098, Kiel, Germany.
Prev Vet Med. 2021 Mar;188:105280. doi: 10.1016/j.prevetmed.2021.105280. Epub 2021 Jan 25.
The inclusion of edge weights can add valuable insights in the spreading processes within trade networks and may identify factors influencing the final epidemic size. The aim of the study was to evaluate the effect of different network versions on the outcome of an epidemiological model. The weighted network versions included the number of trade contacts (A), the sum of delivered livestock (B) and the mean number of delivered livestock per trade contact (C). Furthermore, other factors, e.g. transmission probability and farm type of primary outbreak, were tested for their impact on the final epidemic size. From 2013-2014, data from a pig trade network in Northern Germany was recorded containing 678 farms connected by 1,018 directed edges. An epidemiological model was implemented considering a higher probability of disease spread for edges with a higher weight for each of the combinations between network version and transmission probability. Only transmission routes following the network structure were considered for disease transmission. The outcome of the epidemiological model (number of infected farms) was tested with a generalized linear mixed model including the fixed effects network version (unweighted, A, B, C), transmission probability and farm type of primary outbreak (breeding farm, farrowing farm, finishing farm, farrow-to-finishing farm, unknown) as well as all twofold interactions. The results revealed that all fixed effects as well as all twofold interactions were significant (p ≤ 0.05), i.e. in the following only the impact of the interactions on the number of infected farms can be interpreted. Network versions B and C showed in all combinations the highest number of infected farms independent of the underlying transmission probability. The unweighted network and network version A showed a significant increase of infected farms with increasing transmission probability. All interactions including the farm type of primary outbreak revealed a significant higher number of infected farms for farm types located at the beginning of the production chain, e.g. breeding farms. These farm types reached also more other farms in 1-4 steps compared to farm types located near to the end of the production chain. The inclusion of edge weights has a significant effect on the outcome of epidemiological models and dependent on the chosen edge weight the results need to be interpreted accordingly.
纳入边缘权重可以为贸易网络中的传播过程提供有价值的见解，并可能确定影响最终疫情规模的因素。本研究旨在评估不同网络版本对流行病学模型结果的影响。加权网络版本包括贸易接触次数（A）、交付牲畜的总和（B）和每笔贸易接触交付牲畜的平均数量（C）。此外，还测试了其他因素，如传播概率和初级疫情的农场类型，以评估其对最终疫情规模的影响。2013-2014 年，记录了德国北部一个猪贸易网络的数据，其中包含 678 个农场，通过 1018 条有向边连接。实施了一个流行病学模型，考虑到每种网络版本和传播概率的组合，边缘权重较高时疾病传播的概率更高。仅考虑遵循网络结构的传播途径进行疾病传播。使用广义线性混合模型测试流行病学模型的结果（感染农场的数量），该模型包括固定效应网络版本（无权重、A、B、C）、传播概率和初级疫情的农场类型（繁殖场、产仔场、育肥场、产仔育肥场、未知）以及所有双重交互作用。结果表明，所有固定效应以及所有双重交互作用均具有统计学意义（p≤0.05），即以下仅能解释相互作用对感染农场数量的影响。网络版本 B 和 C 在所有组合中均显示出最高数量的感染农场，独立于潜在的传播概率。无权重网络和网络版本 A 显示出感染农场数量随着传播概率的增加而显著增加。包括初级疫情的农场类型在内的所有相互作用表明，位于生产链开始的农场类型（如繁殖场）的感染农场数量更高。这些农场类型与位于生产链末端附近的农场类型相比，在 1-4 步中可以到达更多的其他农场。边缘权重的纳入对流行病学模型的结果有显著影响，并且取决于所选择的边缘权重，需要相应地解释结果。
