Modelling and assessing additional transmission routes for porcine reproductive and respiratory syndrome virus: Vehicle movements and feed ingredients

Abstract Accounting for multiple modes of livestock disease dissemination in epidemiological models remains a challenge. We developed and calibrated a mathematical model for transmission of porcine reproductive and respiratory syndrome virus (PRRSV), tailored to fit nine modes of between‐farm transmission pathways including: farm‐to‐farm proximity (local transmission), contact network of batches of pigs transferred between farms (pig movements), re‐break probabilities for farms with previous PRRSV outbreaks, with the addition of four different contact networks of transportation vehicles (vehicles to transport pigs to farms, pigs to markets, feed and crew) and the amount of animal by‐products within feed ingredients (e.g., animal fat or meat and bone meal). The model was calibrated on weekly PRRSV outbreaks data. We assessed the role of each transmission pathway considering the dynamics of specific types of production (i.e., sow, nursery). Although our results estimated that the networks formed by transportation vehicles were more densely connected than the network of pigs transported between farms, pig movements and farm proximity were the main PRRSV transmission routes regardless of farm types. Among the four vehicle networks, vehicles transporting pigs to farms explained a large proportion of infections, sow = 20.9%; nursery = 15%; and finisher = 20.6%. The animal by‐products showed a limited association with PRRSV outbreaks through descriptive analysis, and our model results showed that the contribution of animal fat contributed only 2.5% and meat and bone meal only .03% of the infected sow farms. Our work demonstrated the contribution of multiple routes of PRRSV dissemination, which has not been deeply explored before. It also provides strong evidence to support the need for cautious, measured PRRSV control strategies for transportation vehicles and further research for feed by‐products modelling. Finally, this study provides valuable information and opportunities for the swine industry to focus effort on the most relevant modes of PRRSV between‐farm transmission.


INTRODUCTION
Porcine reproductive and respiratory syndrome virus (PRRSV) remains a major economic burden in North America (Holtkamp et al., 2013) as it continues to spread across multiple pig-producing companies Jara et al., 2020;Sanhueza et al., 2019). A recent study developed a mathematical model to reconstruct the between-farm PRRSV dynamics to reveal the role of between-farm pig movements, farm-to-farm proximity and the continued circulation of PRRSV within infected sites (named as re-break) on PRRSV transmission . Despite the promising results, the study did not fully consider indirect contacts through between-farm transportation vehicles (e.g., vehicles transporting pigs, feed or farm personnel) contact networks, which has been previously described as one of the major modes of between-farm transmission of diseases in swine (Büttner & Krieter, 2020;Niederwerder, 2021;Porphyre et al., 2020), such as PRRS (Dee et al., 2002Pitkin et al., 2009; and African swine fever (ASF) (Gao et al., 2021;Gebhardt et al., 2021).
Detailed data regarding transportation vehicle movement and routes, coming in and out pig premises, can be difficult to obtain, which indeed could help explaining the lack of models considering this transmission pathway (Bernini et al.,  farms such as the studies by Wiltshire, 2018, or observed truck movements such as the study by Büttner (2020) using between-farms movements in Germany. The potential of viral stability on vehicle surfaces has been demonstrated to be dependent on environmental conditions such as temperature, pH, moisture and vehicle disinfection procedures (Dee et al., 2002(Dee et al., , 2003Jacobs et al., 2010).
For example, Dee et al. (2002) isolated PRRSV under field conditions from surfaces such as concrete, floor mats and fomites between 2 and 4 h after surface contamination. PRRSV has been shown to be more stable at low temperatures (−20 to −70 • C), surviving for long periods of time (>4 months) (Benfield et al., 1992), and becoming unstable as the temperature increases (Jacobs et al., 2010). In addition, dry conditions, low pH ranging between 5 and 7 (Benfield et al., 1992), iodine, quaternary ammonium or chlorine compounds used in vehicle disinfection were successful in inactivating PRRSV (Shirai et al., 2000). Thus, if environmental conditions favour PRRSV survivability and the vehicles are poorly cleaned and disinfected, the potential for pathogens to disseminate within highly connected networks could indeed play a major role in disease spread (Büttner & Krieter, 2020;Gebhardt et al., 2021).
In addition to transportation movements, contaminated feed could represent a possible route for pathogen transmission (Gebhardt et al., 2021;Niederwerder, 2021), but the probability of PRRSV transmis-sion through feed has been described as relatively low (Blázquez et al., 2020;Cochrane et al., 2017;Ochoa et al., 2018). However, a report by Dee et al. (2020), demonstrated under experimental conditions that pigs which consumed pellet feed contaminated with 1 × 10 5 TCID 50 /ml of PRRSV became infected. As such, cross-contamination of pellet feed may occur when coming into direct contact with contaminated fomites or feed mill workers after the pelleting process (Niederwerder, 2021). In addition, it is important to acknowledge that inadequate temperature applied during the pelleting process could reduce the probability to inactivate PRRSV from contaminated feed ingredients, as observed in an experimental study with porcine epidemic diarrhea virus (Cochrane et al., 2017). In North America, most feed formulations include some animal by-products, such as animal fat, dried plasma or meat and bone meal in order to increase growth performance (Lewis & Southern, 2001). Without adequate processes to inactivate PRRSV, these ingredients could potentially be a source of contamination and later infection. Magar and Larochelle (2004) surveyed two Canadian slaughterhouses and found 4.3% of animal serum samples and 1.2% of the meat samples were positive for PRRSV by polymerase chain reaction. The same study also demonstrated that the consumption of contaminated raw animal by-products caused infection in pigs (Magar & Larochelle, 2004).
In this study, we built a novel mathematical model of PRRSV transmission tailored to nine modes of between-farm propagation: local transmission by the farm-to-farm proximity, between-farm animal and re-break for farms with previous PRRSV outbreaks ( Galvis et al., 2022), with the addition of between-farm vehicle movements (feed, shipment of live pigs between farms and to slaughterhouses and farm personnel [crews]), and the quantity of animal by-products which was restricted to animal fat, meat and bone meal in pig feed ingredients. The model was used to estimate the weekly number of new PRRSV outbreaks and their spatial distribution, which were compared to available data, and to quantify the contribution of each transmission route.

Databases
In this study, we used weekly PRRSV records captured by the Mor- which by the information we collected correspond to the movement of additional personnel needed for vaccination, pig loading and unloading among other activities which included power washing ( Figure 1).
Each movement batch included a unique identification number, speed, date and time along with coordinates of each vehicle location recorded every 5 s. A vehicle visit was defined as a vehicle coordinate (latitude and longitude) and speed of zero km/h for at least 5 min within a radius of 1.5 km of any farm or cleaning station (time and distance radius selected after discussion with personnel in charge of vehicle logistics and data observation). In case more than one farm was located within a 1.5 km radius, we assumed all these farms were at-risk of transmission, and therefore the vehicle contacted all of them. It is worth noting that in some cases where farms are located at distances <1.5 km from other farms, it is because they belong to the same pig production (personal communication). We calculated the time in minutes the vehicle remained within each farm's perimeter and the vehicle contact networks between the farms was built considering the elapsed time a vehicle visited two or more different farms (Figure 1). To accommodate PRRSV survivability in the environment, we considered two seasons (cold and warm weather) based on previous literature (Dee et al., 2002;Jacobs et al., 2010). Under laboratory conditions, it was reported that PRRSV preserved stability for more than 72 h when temperatures oscillated between 4 and 10 • C (cold temperatures) and less than 24 h when temperatures were equal or higher than 20 • C (warm temperatures) (Jacobs et al., 2010). Thus, an edge among two different farms was recorded if the elapsed time the vehicle visited both farms was less than 72 or 24 h, for the cold and warm seasons, respectively.
However, we did not consider the formation of edges between con-

Between-farm animal and transportation vehicles movement
The networks formed by movement of live pigs transported between farms and four types of transportation vehicles visiting farms were reconstructed and analyzed. A set of network metrics, including size, general properties and heterogeneity at node level, was evaluated for each directed static and temporal network (Table S1 for terminology and network metric description). To determine if the static networks of pig and vehicle movements could represent the temporal variation of the between-farm contacts over a year, we calculated the causal fidelity (Lentz et al., 2016). Briefly, causal fidelity quantifies the error of the static representation of temporal networks through a ratio among the number of paths between both representations. Thus, a casual fidelity of 100% would mean that a temporal network is well represented by its static counterpart, and conversely, a value close to 0% means the network should not be considered as a static system (Lentz et al., 2016). We then estimated whether farms with PRRSV outbreaks records were more frequently connected with other infected farms through the ingoing and outgoing contact chain compared with farms without PRRSV records. Finally, we estimated if the time transportation vehicles remained within farms premises was higher in the farms with PRRSV outbreaks compared with farms without PRRSV breaks.
The association for the contact chain and the time the vehicles stayed in the farms with PRRSV outbreaks was evaluated through a Mann-Whitney test.

Animal by-products in feed ingredients
We calculated the total amounts of animal fat, pig plasma, animal protein blend 58%, protein blend (animal protein blend and protein blend was made of a combination of ingredients such as meat meal, corn germ meal, hominy and dried distillers grains with solubles), and meat and bone meal present in each of the 23 feed formulations delivered to farms with and without PRRSV outbreaks in 2020 ( Figures S2 and S3).
In order to further evaluate the association between PRRSV outbreaks and the delivery of feed with animal by-products, we performed a logistic regression analysis for each farm type and ingredient in which the response variable was positive or negative for PRRSV from 1 January 2020 to 31 December 2020, and the predictor was the amount of animal by-product divided by the farm's pig capacity to avoid confusion by the farm size.

Transmission model
The analysis of spatiotemporal distribution of farm-level PRRSV outbreaks was based on our previously developed stochastic model , which here was extended to include vehicle transportation networks and the delivery of animal by-products. The model was calibrated on the weekly PRRSV outbreaks and considering nine transmission modes including: (1) contact network of discrete pig movements; (2) the local transmission events between neighbouring farms driven by distances among farms; (3) re-break by a previous exposure to PRRSV; indirect contact by vehicles coming into farms, including for (4) feed, animal delivery to (5) farms and (6) market, and (7) (Table S2). Otherwise, farms with outbreaks records were assumed to have low biosecurity levels and H was defined as zero.
The transition from infected to an outbreak farm is estimated through a detection rate f(x) (Figure 2). Thus, the probability that farms transit to outbreak state is assumed to be dependent on the maximum detection probability (L), considered equal to cases reported to MSHMP (MSHMP, 2020), and the average time it takes a farm to detect the disease (x0), assumed to be 4 weeks (estimated from information provided by local swine veterinarians and previous literature) (Neira et al., 2017). The proportion of infected and outbreak sow farms that return to a susceptible state is drawn from a Poisson distribution with mean of 41 weeks, which is the average time to stability described elsewhere (Sanhueza et al., 2019). Nursery and finisher farms' transition to susceptible status is driven by pig production movement scheduling of  Table S3) by selecting the 100 particles (number of particles accepted defined according to our computational resources) that best fitted the temporal and spatial distribution of observed PRRSV outbreaks (Figures S8-S10).

Model outputs
The model outputs included (

RESULTS
The comparison among the five networks showed that vehicles transporting feed, pigs to farms, pigs to markets and movement of crews were significantly more connected than the pig movement network ( of the farms from that company, whereas companies A and C showed a low level of connectivity with the LSCC representing less than 1% of the farms. Comparing pig movement networks also showed that company B had the highest edge density of .013, followed by company C (edge density of = .005) and company A the lowest (edge density of = .002).
The vehicles transporting feed static network had a median indegree and out-degree of 319 and 304, respectively, which was the highest in comparison with vehicles transporting pigs to farms, pigs to markets and vehicles used in the transportation of crew (Table 1 and Figures S11 and S12). The networks of vehicles transporting pigs to farms and crew had a median in-degree and out-degree ranging between 14 and 21, whereas vehicles transporting pigs to markets and pig movements for all three companies showed median in-degree and out-degree less than 7 (Table 1). The network of vehicles transporting pigs to farms showed the highest median betweenness centrality, followed by vehicles transporting feed, vehicles transporting pigs to markets and then crew networks, whereas pig movements had the lowest betweenness ( Figure S13). Interestingly, despite the network of vehicles transporting feed being more densely connected, the network of vehicles transporting pigs to farms showed the highest median betweenness centrality values, indicating that this network has the highest number of shortest paths by farm to connect other farms (Table 1 and Figure S13). Considering the result from the temporal networks, vehicles transporting feed showed the highest median ingoing and outgoing contact chain (ICC and OCC) (Table S1), which indicates that feed routes create the largest sequential paths over time that allow for more connections between farms than any transportation or pig movements network (Table 1 and Figures S14 and S15

DISCUSSION
In this study, we demonstrated the contribution of nine pathways in PRRSV dissemination dynamics which included pig movements network, farm-to-farm proximity, different types of transportation vehicle networks (vehicles transporting feed, pigs to farms, pigs to markets and crew), the delivery of animal by-products, in particular animal fat and meat and bone meal in the feed and re-break. We demonstrated that the transportation vehicle networks connected more farms than the pig movement networks, therefore between-farm contacts by transportation vehicles have the potential to propagate PRRSV to more sites and more quickly than moving live pigs between farms. Thus, we remark that the greater potential for PRRSV transmission via transportation vehicle networks pose a great challenge to surveillance and effective control of endemic disease in North America and future eradication of possible introduction of foreign animal diseases such as ASF Gao et al., 2021). Our regression results also suggest that the overall volume of animal by-product delivery to the farms was not associated with the PRRSV outbreaks, and our mathematical model results indicated that animal fat and meat and bone meal delivered to sow farms combined contributed to <2.6% farm infection in the simulations.
Our study addresses major gaps in the understanding of how PRRSV propagates between farms by modelling multiple modes of transmission, which expand the understanding of PRRSV propagation, thus far restricted to studies that have only considered the dissemination of PRRSV throughout animal movement networks (Lee et al., 2017;Makau et al., 2021;. Our previous study  and the information about the transmission dynamics of PRRSV (Dee et al., 2002;Jara et al., 2020;Perez et al., 2015;Pileri & Mateu, 2016;Silva et al., 2019; highlighted limitations of model accuracy and paucity evaluation of PRRSV dissemination by not considering well known modes of transmission, such as indirect contacts formed by transportation vehicles. In this study, we have further extended the previous transmission model , by including six additional transmission routes, including the contact networks formed by transportation vehicles and animal by-products delivered to sow farms via feed ingredients. Our results demonstrate that pig movements and local transmission were the main transmission routes, regardless of farm types (sow, nursery and finisher) (Figure 3). However, the contribution of transportation vehicles used to transfer pigs to farms explained a significant number of infected farms as follows, 20.9% of sow farms, 15% of nurseries and 20.6% of finisher farms. Our examination of feed delivery to farms, more specifically the volume of animal by-products animal fat and meat and bone meal, indicated that this mode did not contribute significantly to PRRSV transmission, contributing to only 2.5% and .03% of the infection in sow farms, respectively. Although our results tend to prove a small role of feed, the approach used in this study is limited by several factors that affect the contribution of feed in the PRRSV dissemination; therefore, these results must be taken with caution (more details in a section below). Finally, for companies B and C, the dominant routes of whereas local transmission mainly affected finishers (Figure 3). However, re-break contributed to a high number of infections that was not observed in our previous study . Overall, our results have also reinforced the findings from previous studies which highlight the role of vehicles in the transmission of infectious diseases that pose a significant threat to or have a particular impact on the swine industry (Dee et al., 2003(Dee et al., , 2007Melmer et al., 2020) and the potential risk of contaminated animal by-products in the feed meals to contribute to between-farm transmission of PRRSV (Dee et al., 2020;Niederwerder, 2021).
From individual vehicle GPS movement data, we reconstructed networks while considering the elapsed time between-farm visits and the time vehicles spent within each farm to define effective contacts among them. In addition, we considered contact between farms to end once a truck drove through a cleaning station (Figure 1), as previous studies suggest that vehicle disinfection can reduce the probability of pathogens' introduction into pig farms, for example, PRRSV (Thakur et al., 2017) and ASFV (Yoo et al., 2021). In the current work, the inclusion of cleaning stations reduced around half the edges of the four types of transportation vehicle networks, which represent valuable information for the analysis of disease transmission given that including or not cleaning stations provide different results of the pathogen dissemination among the farms through vehicles. It is worth to notice that we assumed that the cleaning process was always effective to inactivate PRRSV (Shirai et al., 2000), even though the literature about probability of PRRSV survival on vehicle surfaces after cleaning and disinfection remains limited . Thus, further studies evaluating the presence and infectivity of PRRSV after vehicle cleaning and disinfection are necessary.
Previous studies attempting to model transportation vehicle networks were limited to either static or simulated between-farm contact networks, thus limiting our ability to further compare our networks results Wiltshire, 2018;Sterchi et al., 2019;Porphyre et al., 2020;Yang et al., 2020). However, our result demonstrated that for the four vehicle networks described in this study, the static networks provided a close representation of the actual temporal networks, in which the ratio of the number of paths between the static and temporal network varied from 58% for vehicles transporting pigs to markets to 98.7% for vehicles delivering feed (Table 1). Because of the high fidelity of the vehicle networks, our results demonstrate that the static networks may be sufficient to explain causal paths among farms formed by vehicle movements (Lentz et al., 2016). Although these results were only evaluated by comparing the static and temporal network from a single commercial company and with one year of GPS data, our results strongly suggest that static views of transportation vehicles networks can be used either to describe such networks or to be used in disease transmission models when researchers only have access to a static view of a network.
The transportation vehicle networks were more densely connected than the networks of between-farm pig movements, ranging from 3 to 100 times more connect considering the network of vehicles transporting pigs to markets and feed, respectively. Other studies have also found that vehicle movements between farms used for animal hauling increased the indirect contacts among farms by more than 50% (Porphyre et al., 2020), consequently the network weak connected component became 50% larger (Sterchi et al., 2019). Among the transportation vehicle networks analyzed here, the network of feed deliveries was the most connected; for instance, more than 85% of all farms of company A were connected through sequential paths in the temporal network (ICC and OCC; Table 1). On the contrary, the network of trucks transporting live pigs between farms was less connected, but in our transmission model, it represented between 15% and 20% of the total transmissions. In turn, the probability of transportation vehicles being contaminated with PRRSV is more likely in vehicles transporting animals than feed, mainly because of the direct contact with infected animals. Vehicles transporting pigs to markets could in the same way play a similar risk of contamination as vehicles transporting pigs to farms; however, the former vehicles tend to visit mostly finisher farms with pigs ready for slaughter, thus less likely to re-introduce PRRSV back into the transmission chain by visiting breeding farms (Passafaro et al., 2020). It is worth noting that this is not the case for farms with complete production cycles, such as farrow to finisher farms, in which movements returning from slaughterhouses are likely to pose a great risk (Henry et al., 2018). Our study was also the first to collect and consider in a transmission model the contact networks of vehicles transporting crew between farms. It is known that the number of farm visitors increases the probability of introduction of infectious pathogens (e.g., PRRSV); thus, the movement of additional personnel often involved in loading and unloading pigs have been previously associated with PRRSV dissemination and outbreaks (Dee et al., 2002;Pitkin et al., 2009;Rossi et al., 2017). It is worth noting that in our study, we modelled the consecutive contacts between farms formed by the vehicles used by crew as a route of PRRSV dissemination, by evaluating individual vehicles connecting farms that were visited consecutively rather than the group of crew members, which is known to vary between each farm visit. Therefore, the risk of infection by vehicles transporting crew could be more related to the vehicle itself as fomite, which in turn is likely to represent a lower risk of infection compared with the risk of infection related to the personnel. In general, all four transporting vehicle networks evaluated in this study contributed to PRRSV transmission, similarly to previous studies Rossi et al., 2017;Porphyre et al., 2020;Yang et al., 2020). It is important to remark that the contribution of the networks described above may have been underestimated, mainly because we have not fully considered the effectiveness of cleaning and disinfection to reduce PRRSV contamination in vehicles driving through cleaning stations. The lack of studies measuring the effectiveness of cleaning and disinfections stations in reducing PRRSV and the contribution of additional on-farm biosecurity cleaning and disinfection such as the presence of automatic cleaning stations at the entrance of farms (Dee et al., , 2007Silva et al., 2019) is clearly needed in order to better specify the reduction of such procedures in the force of PRRSV transmission.
The potential propagation of infectious diseases within feed ingredients has been of concern not only to the swine industry but across  Niederwerder, 2021). Despite the concerns about feed as a route of PRRSV transmission, many uncertainties remain, including the minimal infection dosage required to cause disease, the effectiveness of feed processing such as pelleting, extruding and roasting and the use of feed additives (Dee et al., 2020;Niederwerder, 2021). In addition, it is important to mention that feed contamination may also occur within the feed mill facility either by contaminated environments, person-nel, equipment, birds or rodents, or even contaminated trailers coming in and out feed mill facilities (Dee et al., 2020;Gebhardt et al., 2021;Niederwerder, 2021); our model does not explicitly consider such uncertainties nor attempt to account for such complexity. In this study, we assumed that all feed meals with any amount of animal byproducts were still able to cause infection once delivered. In addition, we also assumed that the pelleting process did not eliminate PRRSV contamination, and feed was delivered with enough viral load to cause infection. Even though our results showed a relatively small role of animal by-products (less than 2.6%), there are limitations to our approach and also limited information about the risk and pathways of collateral contamination during or after feed manufacturing. For example, the effect of high temperatures and pressure used during pelleting in inactivating PRRSV remains unknown (Benfield et al., 1992;Van Alstine et al., 1993;Bloemraad et al., 1994;Cochrane et al., 2017); if once such data become available, it will be possible to better assess the role of animal by-products in PRRSV transmission.

Limitations and final remarks
We identify a number of limitations related to the simulated scenarios and data availability. First, our calculation approaches for the con- were included in the model because of the relevance of the local transmission in the company-to-company spread of PRRSV, described in details elsewhere (Jara et al., 2020). The 1.5 km radius used to define when a vehicle visited a farm or cleaning station was a limitation for reconstructing the vehicle networks for sites that were 1.5 km from each other; thus, in some cases, the contacts were counted towards two or more instead of a single farm (median number of neighbours into 1.5 km = 1). A future alternative to reduce such events would require geographic information of each farms' feed bins, for example. Additionally, the on-farm model parameters were oversimplified, since we have based those estimations through historical records of PRRSV outbreaks, in which farms with fewer infections were considered to have better biosecurity levels. Although there are several ways that the current version of PigSpread model can be expanded, the inclusions of specific on-farm biosecurity practices and infrastructure (e.g., present of cleaning and disinfection stations) could not only improve model calibration but also analyze the role of individualized and combined biosecurity on PRRSV dissemination (Sykes et al., 2021).
Another important limitation of our modelling work was the lack of information about the vaccination strategies used by each farm, which could have contributed to the probability of new PRRSV outbreaks . Finally, we highlight that additional studies are necessary to understand the effect of EVI and seasons on the local transmission and to evaluate the performance of the gravity model against other transmission methods, such as density kernels, to fit PRRSV outbreak locations. Despite the limitations, this is the first study modelling simultaneously nine routes involved in PRRSV dissemination dynamics over an entire year of outbreak data. This study is unique because it provides the swine industry and regulatory agencies with robust and essential results about the dynamics of between-farms swine disease transmission and the most relevant routes of transmission, offering a unique opportunity to enhance the control of endemic disease and also prepare for future threats (Herrera-Ibatá et al., 2018;Jurado et al., 2019;Brown et al., 2020).

CONCLUSION
We expanded a previously developed stochastic PRRSV simulation model