Publication:
Nelson, Michael F., and Christopher E. Bone. “Effectiveness of Dynamic Quarantines against Pathogen Spread in Models of the Horticultural Trade Network.” Ecological Complexity 24 (December 2015): 14–28. https://doi.org/10.1016/j.ecocom.2015.07.002.
Background
This was the first project I worked on during my postdoc at the University of Oregon with Chris Bone in the Geography Department.
We both had an interest in the role of the horticulture industry in spreading plant pests and pathogens. We were both very interested in network models at the time, and the two interests came together for this project.
The Sudden Oak Death (SOD) pathogen (Phytophthora ramorum) is a major pathogen of oaks and related species in the forests of northern California. The disease causes bleeding cankers and rapid death of the region’s iconic oaks and tanoaks. The pathogen is known to have spread long distances through horticultural trade.
Modeling
We created 3-tiered network models of the trade relationships between hypothetical growers, wholesaslers, and retailers. The trade models were created using an algorithm that builds scale-free networks via preferential attachment. Connections were allowed between growers to wholesalers and from wholesalers to retailers. Intra-tier edges were allowed in the grower and wholesaler tiers.
A periodic inspection and quarantine algorithm was used to simulate real inspections and quarantines within the trade network. Quarantined nodes were temporarily removed from the network and were allowed to re-enter the network once their level of infection was below the detection threshold.
Figure 1: Example trade network with 400 growers (left nodes), 200 wholesalers (center nodes), and 400 retailers (right nodes). The upper panel shows the intact network. The lower panel shows the network after a prominent grower, wholesaler, and retailer were temporarily removed and placed in quarantine.
Simulations
Several parameters were varied in the simulated networks. One of the main parameters to vary in the simulation was the interval between inspections. They could either be long (50 time steps) or short (10 time steps). The probabilies of transmission (between nodes) and persistence (within a node) were varied. Simulations were run for 250 or 500 time steps over 60 replicate simulated networks depending on the experimental scheme.
Main Findings
The results were complex, but indicated that in general quarantine efforts were most effective when concentrated on the middle tier (the wholesalers). Reducing the connectivity among nodes in the wholesaler tier also reduced the mean retailer infection rates. We also found that grower hubs (growers with the largest numbers of connections) tended to drive the temporal dynamics of the whole system.
Figure 7: This figure shows how the grower tier (on the x-axis in the upper row of panels, on the dashed line in the lower row) drives the dynamics of the system. For example, in panel b you can see how the infection rate increased in the wholesaler tier following increases in the growers (dashed line). The asterisks show when the quarantine was applied to the largest individual in each tier. The infection prevalence falls in each tier in the time steps following the quarantine, but the most dramatic falls are after the quarantine of the largest grower.
Conclusions
Real horticulture trade networks are likely more complex than these simulations, however the general results of the importance of large growers was a common pattern throughout all the simulated scenarios.