Annie Jonsson

Network analysis of cattle and pig movements in Sweden : Measures relevant for disease control and risk based surveillance

Registration of cattle and pig movements is mandatory in Sweden and all registered movements between farms in the years 2006-2008 were investigated using network analysis. The networks were analysed as monthly and yearly networks, separately per species and with the two species together. Measures that have been previously discussed in relation to outbreaks and disease control were calculated; moreover a measure of the ingoing infection chain was constructed. The ingoing infection chain captures ingoing contacts through other holdings, taking the temporal aspect and sequence of the movements into account. The distribution of the contacts among the holdings was skewed. Many farms had few or no contacts, while others had many, a pattern which has also been described from other countries. The cattle network and the combined network showed a recurring seasonal pattern, while this was not seen in the pig network. The in-degree was not equivalent to the ingoing infection chain; there were holdings with limited direct contacts, but a large number of indirect contacts. The ingoing infection chain could be a useful measure when setting up strategies for disease control and for risk based surveillance as it identifies holdings with many contacts through live animal movements and thus at potentially higher risk for introduction of contagious diseases.

Estimation of distance related probability of animal movements between holdings and implications for disease spread modeling.

Between holding contacts are more common over short distances and this may have implications for the dynamics of disease spread through these contacts. A reliable estimation of how contacts depend on distance is therefore important when modeling livestock diseases. In this study, we have developed a method for analyzing distant dependent contacts and applied it to animal movement data from Sweden. The data were analyzed with two competing models. The first model assumes that contacts arise from a purely distance dependent process. The second is a mixture model and assumes that, in addition, some contacts arise independent of distance. Parameters were estimated with a Bayesian Markov Chain Monte Carlo (MCMC) approach and the model probabilities were compared. We also investigated possible between model differences in predicted contact structures, using a collection of network measures. We found that the mixture model was a much better model for the data analyzed. Also, the network measures showed that the models differed considerably in predictions of contact structures, which is expected to be important for disease spread dynamics. We conclude that a model with contacts being both dependent on, and independent of, distance was preferred for modeling the example animal movement contact data.

Generating Structure Specific Networks

Theoretical exploration of network structure significance requires a range of different networks for comparison. Here, we present a new method to construct networks in a spatial setting that uses spectral methods in combination with a probability distribution function. Nearly all previous algorithms for network construction have assumed randomized distribution of links or a distribution dependent on the degree of the nodes. We relax those assumptions. Our algorithm is capable of creating spectral networks along a gradient from random to highly clustered or diverse networks. Number of nodes and link density are specified from start and the structure is tuned by three parameters (γ, σ, κ). The structure is measured by fragmentation, degree assortativity, clustering and group betweenness of the networks. The parameter γ regulates the aggregation in the spatial node pattern and σ and κ regulates the probability of link forming.

SpecNet : a spatial network algorithm that generates a wide range of specific structures

Network measures are used to predict the behavior of different systems. To be able to investigate how various structures behave and interact we need a wide range of theoretical networks to explore. Both spatial and non-spatial methods exist for generating networks but they are limited in the ability of producing wide range of network structures. We extend an earlier version of a spatial spectral network algorithm to generate a large variety of networks across almost all the theoretical spectra of the following network measures: average clustering coefficient, degree assortativity, fragmentation index, and mean degree. We compare this extended spatial spectral network-generating algorithm with a non-spatial algorithm regarding their ability to create networks with different structures and network measures. The spatial spectral network-generating algorithm can generate networks over a much broader scale than the non-spatial and other known network algorithms. To exemplify the ability to regenerate real networks, we regenerate networks with structures similar to two real Swedish swine transport networks. Results show that the spatial algorithm is an appropriate model with correlation coefficients at 0.99. This novel algorithm can even create negative assortativity and managed to achieve assortativity values that spans over almost the entire theoretical range.

Improvement of animal welfare by strategic analysis and logistic optimisation of animal slaughter transportation

The transportation of animals to slaughterhouses is a major welfare concern. The number of slaughterhouses has decreased over time in Europe due to centralisation. This is expected to increase tran ...

Approximations of population growth in a noisy environment: on the dichotomy of non-age and age structure

By simulations of population growth exposed to environmental noise, we compared realised long-run growth rate of age structured populations of four different life histories, with four approximations. One approximation used a non-structured population model, including specific population growth rates for each time step, determined by actual vital rates, while the other three used age-structured data to estimate a ‘mean’ growth rate, then applicable for all time steps. In general, approximations were reasonable accurate. Yet some were completely erroneous and inaccurate enough to move stationary populations to become species on the red list as an endangered species according to International Union for Conservation of Nature (IUNC). The inaccuracies depended, in the following decreasing order, on: life history, what part of the demography the noise was acting on, and noise colour. The non-structured growth approximation had smaller errors with red noise while the three age-structured approximations had their largest errors with red noise. Since it is generally understood that the most common noise in nature is red noise, we conclude that the non-structured approximation will be the best predictor of population growth in most cases. We also conclude that evenness in distribution over age classes is a possible predictor for the sensitivity of long-run growth rate to type of approximation and therefore a promising object for further studies. Finally, our results indicate that in general, more focus ought to be on reducing the error in the data collection on population densities, especially for studies over longer time periods, than of collecting age-specific data.

Route optimization as an instrument to improve animal welfare and economics in pre-slaughter logistics

Each year, more than three million animals are transported from farms to abattoirs in Sweden. Animal transport is related to economic and environmental costs and a negative impact on animal welfare. Time and the number of pick-up stops between farms and abattoirs are two key parameters for animal welfare. Both are highly dependent on efficient and qualitative transportation planning, which may be difficult if done manually. We have examined the benefits of using route optimization in cattle transportation planning. To simulate the effects of various planning time windows and transportation time regulations and number of pick-up stops along each route, we have used data that represent one year of cattle transport. Our optimization model is a development of a model used in forestry transport that solves a general pick-up and delivery vehicle routing problem. The objective is to minimize transportation costs. We have shown that the length of the planning time window has a significant impact on the animal transport time, the total driving time and the total distance driven; these parameters that will not only affect animal welfare but also affect the economy and environment in the pre-slaughter logistic chain. In addition, we have shown that changes in animal transportation regulations, such as minimizing the number of allowed pick-up stops on each route or minimizing animal transportation time, will have positive effects on animal welfare measured in transportation hours and number of pick-up stops. However, this leads to an increase in working time and driven distances, leading to higher transportation costs for the transport and negative environmental impact.

Synthetic generation of spatial graphs: TORRA et al.

Graphs can be used to model many different types of interaction networks, for example, online social networks or animal transport networks. Several algorithms have thus been introduced to build graphs according to some predefined conditions. In this paper, we present an algorithm that generates spatial graphs with a given degree sequence. In spatial graphs, nodes are located in a space equiped with a metric. Our goal is to define a graph in such a way that the nodes and edges are positioned according to an underlying metric. More particularly, we have constructed a greedy algorithm that generates nodes proportional to an underlying probability distribution from the spatial structure, and then generates edges inversely proportional to the Euclidean distance between nodes. The algorithm first generates a graph that can be a multigraph, and then corrects multiedges. Our motivation is in data privacy for social networks, where a key problem is the ability to build synthetic graphs. These graphs need to satisfy a set of required properties (e.g., the degrees of the nodes) but also be realistic, and thus, nodes (individuals) should be located according to a spatial structure and connections should be added taking into account nearness.