Disease spread through animal movements: a static and temporal network
  analysis of pig trade in Germany

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Abstract

Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The central question is how infectious diseases can potentially spread within the system of trade contacts. We address this question by analyzing the underlying network of animal movements. Methodology/Findings: The considered pig trade dataset spans several years and is analyzed with respect to its potential to spread infectious diseases. Focusing on measurements of network-topological properties, we avoid the usage of external parameters, since these properties are independent of specific pathogens. They are on the contrary of great importance for understanding any general spreading process on this particular network. We analyze the system using different network models, which include varying amounts of information: (i) static network, (ii) network as a time series of uncorrelated snapshots, (iii) temporal network, where causality is explicitly taken into account. Findings: Our approach provides a general framework for a topological-temporal characterization of livestock trade networks. We find that a static network view captures many relevant aspects of the trade system, and premises can be classified into two clearly defined risk classes. Moreover, our results allow for an efficient allocation strategy for intervention measures using centrality measures. Data on trade volume does barely alter the results and is therefore of secondary importance. Although a static network description yields useful results, the temporal resolution of data plays an outstanding role for an in-depth understanding of spreading processes. This applies in particular for an accurate calculation of the maximum outbreak size.

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Error and attack tolerance of complex networks

Albert-László Barabási, Hawoong Jeong, Reka Albert (2000)

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.

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Assortative mixing in networks

M. Newman (2002)

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.

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The economic impacts of foot and mouth disease – What are they, how big are they and where do they occur?

T.J.D. Knight-Jones, J Rushton (2013)

Although a disease of low mortality, the global impact of foot and mouth disease (FMD) is colossal due to the huge numbers of animals affected. This impact can be separated into two components: (1) direct losses due to reduced production and changes in herd structure; and (2) indirect losses caused by costs of FMD control, poor access to markets and limited use of improved production technologies. This paper estimates that annual impact of FMD in terms of visible production losses and vaccination in endemic regions alone amount to between US$6.5 and 21 billion. In addition, outbreaks in FMD free countries and zones cause losses of >US$1.5 billion a year. FMD impacts are not the same throughout the world: 1. FMD production losses have a big impact on the world's poorest where more people are directly dependent on livestock. FMD reduces herd fertility leading to less efficient herd structures and discourages the use of FMD susceptible, high productivity breeds. Overall the direct losses limit livestock productivity affecting food security. 2. In countries with ongoing control programmes, FMD control and management creates large costs. These control programmes are often difficult to discontinue due to risks of new FMD incursion. 3. The presence, or even threat, of FMD prevents access to lucrative international markets. 4. In FMD free countries outbreaks occur periodically and the costs involved in regaining free status have been enormous. FMD is highly contagious and the actions of one farmer affect the risk of FMD occurring on other holdings; thus sizeable externalities are generated. Control therefore requires coordination within and between countries. These externalities imply that FMD control produces a significant amount of public goods, justifying the need for national and international public investment. Equipping poor countries with the tools needed to control FMD will involve the long term development of state veterinary services that in turn will deliver wider benefits to a nation including the control of other livestock diseases.