Modelling farm-to-farm disease transmission through personnel movements: from visits to contacts, and back

Infectious diseases in livestock can be transmitted through fomites: objects able to convey infectious agents. Between-farm spread of infections through fomites is mostly due to indirect contacts generated by on-farm visits of personnel that can carry pathogens on their clothes, equipment, or vehicles. However, data on farm visitors are often difficult to obtain because of the heterogeneity of their nature and privacy issues. Thus, models simulating disease spread between farms usually rely on strong assumptions about the contribution of indirect contacts on infection spread. By using data on veterinarian on-farm visits in a dairy farm system, we built a simple simulation model to assess the role of indirect contacts on epidemic dynamics compared to cattle movements (i.e. direct contacts). We showed that including in the simulation model only specific subsets of the information available on indirect contacts could lead to outputs widely different from those obtained with the full-information model. Then, we provided a simple preferential attachment algorithm based on the probability to observe consecutive on-farm visits from the same operator that allows overcoming the information gaps. Our results suggest the importance of detailed data and a deeper understanding of visit dynamics for the prevention and control of livestock diseases.


S2. Number of contacts per visit
In the main text we showed the results of the analysis of the distribution of the indirect contacts generated by veterinarians' visits (Figure 2). In Figure S2.1, we showed the best fitting sensitivity analysis for different values of xmin, which represents the distribution's heavy-tailed behaviour positive lower bound (i.e. > 0).
Here, we performed the analysis of the distribution of the number of contacts per visit provided in the main text assuming four alternative contamination period lengths: 0, 7, 21, and 28 days. We showed the results of the fitting procedures in Figure S2.2, while in Figure S2.3 we showed the results of the Kolmogorov-Smirnov and Vuong's tests for a range of xmin values.
In Table S2.1 we reported the values of the number of contacts per visit distribution for all the considered values of h. Moreover, we showed the parameters of the best fitted discrete log-normal and power-law distributions, as these are the distributions which provided the best fit to the data.
In the main text we showed how a simulation model that assumed one contact per visits was unable to produce similar epidemic dynamics compared with a the simulation model using the original data (main text Figure 3). To evaluate the potential effect of the contamination period on this result, we repeated the analysis for an h value of 0 days (as opposed to the benchmark of 14 days); this was equivalent to assuming that potentially infectious contacts only occur within the same day of the original infected farm visit. As showed in Figure S2.4, when h = 0, the simulation model assuming one indirect contact per visit overestimated the extent of a potential epidemic, in contrast to the h = 14 case (see main text Figure 3) in which the outbreaks extent were underestimated.

S3. JI matrix and visits per veterinarian alternative distributions
In Figure S3.1 we showed the Jaccard Index matrix, in a grey scale gradient (white correspond to 0, black correspond to 1). For each pair of farms i and j their JIij was calculated following the Jaccard index as showed in the Methods section of the main text. The values of the JI matrix were used as probability for two farm to be have an indirect contact in the cluster rewiring model (CR).
In the main text, we presented an analysis in which we investigated the role of the veterinarian-farm relationship. We re-assigned the observed on-farm visits to different veterinarians in two ways, randomly and following a preferential attachment criteria (i.e. it is more likely for a farm to be visited by a veterinarian that already visited it, see main text for details). In these, we maintained the distribution of the number of visits per veterinarian by assuming that each veterinarian did the same exact number of visits that we observed in our dataset. As showed in Figure S3.2, this distribution was very skewed. To test the potential role of this, we did a further analysis in which we assumed two alternative distributions for the number of visits per veterinarian: uniform and normal. One example for each distribution was showed in Figure S3.3. Using the previous criteria, we firstly assigned to each veterinarian a new number of visits, and then we coupled the veterinarians with the observed on-farm visits following the preferential attachment algorithm. As in the analysis presented in the main text, the first visit in each farm was assigned to a random veterinarian, while from the second on there was a 77% probability to be assigned to a veterinarian that had already visited the farm (see main text's Method section for details on this probability calculation). Thus, we simulated the epidemic spread within the system using the indirect contacts obtained as described.
As showed in Figure S3.4, by using alternative visits per veterinarian distributions we failed to reproduce the same patterns observed in the original simulations. In both cases, the extent of an epidemic was underestimated, as well as the number of outbreaks able to generate secondary cases.         The matrix representing the observed values of the farms-veterinarian Jaccard Index JIij (see main text section 2.5, (3)) calculated for each pair of farms i and j (on x-and y-axes, matrix is symmetric). Grey scale represents JI values between 0 (white) and 1 (black), and they are square rooted for visualization purposes.