Impact of Network Activity on the Spread of Infectious Diseases through the German Pig Trade Network

Karin Lebl, Hartmut H. K. Lentz, Beate Pinior, Thomas Selhorst

The trade of livestock is an important and growing economic sector, but it is also a major factor in the spread of diseases. The spreading of diseases in a trade network is likely to be influenced by how often existing trade connections are active. The activity α is defined as the mean frequency of occurrences of existing trade links, thus 0 < α ≤ 1. The observed German pig trade network had an activity of α = 0.11, thus each existing trade connection between two farms was, on average, active at about 10% of the time during the observation period 2008-2009. The aim of this study is to analyze how changes in the activity level of the German pig trade network influence the probability of disease outbreaks, size, and duration of epidemics for different disease transmission probabilities. Thus, we want to investigate the question, whether it makes a difference for a hypothetical spread of an animal disease to transport many animals at the same time or few animals at many times. A SIR model was used to simulate the spread of a disease within the German pig trade network. Our results show that for transmission probabilities <1, the outbreak probability increases in the case of a decreased frequency of animal transports, peaking range of α from 0.05 to 0.1. However, for the final outbreak size, we find that a threshold exists such that finite outbreaks occur only above a critical value of α, which is ~0.1, and therefore in proximity of the observed activity level. Thus, although the outbreak probability increased when decreasing α, these outbreaks affect only a small number of farms. The duration of the epidemic peaks at an activity level in the range of α = 0.2-0.3. Additionally, the results of our simulations show that even small changes in the activity level of the German pig trade network would have dramatic effects on outbreak probability, outbreak size, and epidemic duration. Thus, we can conclude and recommend that the network activity is an important aspect, which should be taken into account when modeling the spread of diseases within trade networks.