Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks

Conventional epidemiological studies of infections spreading through trade networks, e.g. via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic–epidemiological risks in networks underlying pathogen propagation and trade.


A.1 Standard indicators of epidemiological risk: definitions and implications for epidemics
We define standard indicators to assess epidemiological risk for networks: the proportion of agents belonging to the largest strongly connected component (LSCC) and betweenness centrality.
The proportion of agents belonging to the LSCC is a standard proxy to assess both the probability of an outbreak and the epidemic final size [e.g. 1,2]. Formally, the LSCC is the largest set of agents that can be reached by any other agent by following the direction of links over a time period T . The larger the fraction of agents belonging to 15 the LSCC, the larger the epidemiological risk. Since we calculate the proportion of agents belonging to the LSCC for each market category, we can estimate the contribution of each market category to the global epidemiological risk.
The betweenness centrality of an agent a, denoted BC a , is the fraction of shortest path lengths that passes through a. The shortest path length from agent i to agent j is the smallest number of directed links needed to reach j from i. The larger BC a , the larger the epidemiological risk of agent a [e.g. 3,4]. Formally, BC a , here normalised to account 20 for networks differing in total number of agents, is given by: where σ st (T ) and σ sat (T ) are the number of shortest paths from agent s to agent t and the number of shortest paths from s to t passing through a during a time period T respectively. Since calculating shortest paths on large networks is computationally intensive, we approximate BC a at order 3, i.e. we only consider shortest paths of length 3 or less.
A.2 Multiple-criteria decision analysis based on the average infection chain as a proxy for prevention-25 effectiveness An alternative proxy to assess the effectiveness of preventive strategies: the average infection chain We alternatively measure effectiveness, for differing strategies S, as the percentage decrease of the average infection chain as function of the fraction of agents to target F n . For a given time period T = [t 1 ; t 2 ], the out-going infection chain of a seller i (in-going infection chain of a demander j respectively) is the number of demanders that can be 30 reached and hence infected from i by following temporally-compatible links (the number of sellers leading to j and from which j can hence be infected by following temporally-compatible links respectively). The out-going infection chain is calculated forwards in time (from t 1 to t 2 ), while the in-going infectious chain is calculated backwards in time (from t 2 to t 1 ). Both the out-and in-infection chains are epidemiological proxies [5,6]. Following [7], we focus here on the average infectious chain, which is indifferently given, for a given T , by the the average in-going infection chain 35 or the average out-going infection chain as calculated over all nodes. In contrast with the largest strongly connected component, the average infection chain takes into account the sequentiality of the dates at which exchanges occur over period T . For each strategy explored, the percentage decrease of the average infection chain is evaluated at increasing values of F n and we carry out 100 runs of random targeting.

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Since we keep track of time, we further distinguish two types of interventions for a given S: early interventions where all the F n agents are surveilled at the beginning of the time period T where the strategy is evaluated, and partly delayed interventions where the first half of the ordered F n agents is targeted at t 1 and the second half at (t 1 + t 2 ) 2.
Selection of geographical subsets of the cattle dataset to assess percentage decrease of the average infection chain 45 Even when carfully optimised, the evaluation of average infection chains remains computationally-intensive [8]. We hence restrict their calculations to the cattle market for small geographical scales, here French Départements (Dpt). We consider, on the one hand, exchanges occurring within the Ille-et-Vilaine Dpt and with the rest of the world (Dpt 35 + ROW) and, on the one hand, exchanges occurring within the Saône-et-Loire Dpt and the rest of the world (Dpt 71+ ROW). Dpt 35 and Dpt 71 are the largest French Dpt for dairy and beef production respectively (Tables S1-S2).   S1). For swine, we only have access to deliveries occurring during year 2010, so we can not explore stability of market categories on a yearly scale.

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Over years 2005-2009, flow polarity is more variable than flow share ( Fig. S1A-B). Relative summaries such as flow share are expected to be highly stable over time and for any temporal scale used to calculate them [9].

B.2 Standard indicators of epidemiological risk in relation with market categories
In addition to the proportion of agents belonging to the largest strongly connected component (Fig. 2 in the main text), we calculate the betweenness centrality, an additional standard indicator for epidemiological risk for both cattle and swine markets. We show how this measure scales with market categories, i.e. with flow polarity and flow share. For both cattle and swine, the betweenness centrality increases with flow share (Fig. S2), implying a larger epidemiological risk associated with leaders compared with nichers. For a given flow share, the average betweenness centrality tends to be larger for agents with negligible flow polarity: wholesalers are probably stronger epidemiological drivers than suppliers, a finding in agreement with the theoretical results reported in [10,11]. Measuring prevention-effectiveness based on the largest strongly connected component, we find, by carrying-out percolation experiments on the cattle market (Fig. 4 in the main text), that targeting suppliers-nichers first (SN strategy) induces lower relative flow-cost to the regulator and lower market distortions than targeting wholesalersleaders first (WL strategy).
Here we test whether these findings stand when prevention-effectiveness is rather measured based on the average 75 infection chain (Section A.2). We also explore impacts of delaying interventions. We focus our analyses on two contrasted geographical subsets of the French cattle market called Départements (Dpt): Dpt 35 (essentially dairy production) and Dpt 71 (essentially beef production). We also consider, for each Dpt, exchanges with the Rest Of the World (ROW). The results remain qualitatively unchanged compared to those reported in the main text for the cattle market (