Date Published: June 10, 2019
Publisher: Public Library of Science
Author(s): Aurore Payen, Lionel Tabourier, Matthieu Latapy, Chiara Poletto.
Infections can spread among livestock notably because infected animals can be brought to uncontaminated holdings, therefore exposing a new group of susceptible animals to the disease. As a consequence, the structure and dynamics of animal trade networks is a major focus of interest to control zoonosis. We investigate the impact of the chronology of animal trades on the dynamics of the process. Precisely, in the context of a basic SI model spreading, we measure on the French database of bovine transfers to what extent a snapshot-based analysis of the cattle trade networks overestimates the epidemic risks. We bring into light that an analysis taking into account the chronology of interactions would give a much more accurate assessment of both the size and speed of the process. For this purpose, we model data as a temporal network that we analyze using the link stream formalism in order to mix structural and temporal aspects. We also show that in this dataset, a basic SI spreading comes down in most cases to a simple two-phases scenario: a waiting period, with few contacts and low activity, followed by a linear growth of the number of infected holdings. Using this portrait of the spreading process, we identify efficient strategies to control a potential outbreak, based on the identification of specific elements of the link stream which have a higher probability to be involved in a spreading process.
Production of dairy and meat products is a major economic field in Europe. Fighting disease spreading is thus a key issue for the protection of economic interests, as well as human health and animal welfare. Among the various routes to infect holdings, such as contamination by wildlife or contacts between herds in pastures, cattle trade movements spread pathogens at national and international levels, and are thus a major way of infection. People and decision makers in Europe have recently become more aware of the problem. In particular, since the Bovine Spongiform Encephalopathy crisis of 1996, each state of the European Union has to identify every bovine on its territory and to register cattle trade movements. The Base de Données Nationale d’Identification (BDNI) database, which is the focus of this work, is the French enforcement of this decision. This kind of data is characterized by the availability of temporal information through the record of dated cattle exchanges. The aim of this study is to fully capture the importance of temporal information when modeling disease spreading in order to evaluate potential outbreak sizes and to be able to characterize spreading speeds.
Throughout this work, we deal with the BDNI, which records bovine trade movements in France. We have access to eleven years of data from 2005 to 2015. The access to the BDNI is not public, but can be obtained through a specific agreement with the French ministry of agriculture. It contains approximately 148 million animal transfers. Animals are often traded in batches, and as we do not model an infection at the animal level, we focus on batch transfers between holdings, which are dated with a daily granularity. Batch sizes are not investigated in this work. Moreover, different types of holdings feature the data: farms, markets, assembly centers, slaughterhouses and knackery premises. Movements to slaughterhouses and knackeries are dead-ends concerning disease propagation, therefore, we exclude them from our data. After this basic preprocessing, there are around 32,600,000 time-labeled batch movements in the dataset. Among the remaining 300.000 holdings, there are 90 markets (0.03%), about 2800 assembly centers (0.9%), and the rest are farms.
In this work, we gave support to the idea that it is crucial to take into account the temporal dimension of data in order to model spreadings in animal trade networks. This point of view is well-spread in the literature, and previous works put forward several arguments in its favor. In the case of the BDNI, we confirmed several aspects of these works, in particular the fact that snapshot-based representations tend to overestimate the sizes of outbreaks, and give a distorted view of the distribution of potential outbreak sizes. Furthermore, we investigated the spreading scenarios encountered, using not only measurements of the outbreak size but also of its speed. We pointed out that our spreading process leads essentially to a unique kind of large-size cascades in the case of the BDNI, well approximated by a two phases model. This model gives a simple picture of the spreading process: during a waiting period, the infection remains nearly silent, then it reaches a tipping point and grows linearly from then on. These observations led us to reconsider several aspects of epidemic control strategies. First, the cost of a strategy should be more appropriately evaluated in terms of the natural unit of a temporal network, that is a triplet of interaction. Second, the impact of an infection model may be assessed with its size but also with its speed, even in the case of our standard deterministic SI model. Finally the strategy itself can be conceived using the epidemic cascades themselves, which proves to be much more efficient that usual node-centrality based strategies, in a retrospective as well as in a predictive context.