Analysis of German BSE Surveillance Data: Estimation of the Prevalence of Confirmed Cases versus the Number of Infected, but Non-Detected, Cattle to Assess Confidence in Freedom from Infection.

Quantitative risk assessments for Bovine spongiform encephalopathy (BSE) necessitate estimates for key parameters such as the prevalence of infection, the probability of absence of infection in defined birth cohorts, and the numbers of BSE-infected, but non-detected cattle entering the food chain. We estimated three key parameters with adjustment for misclassification using the German BSE surveillance data using a Gompertz model for latent (i.e., unobserved) age-dependent detection probabilities and a Poisson response model for the number of BSE cases for birth cohorts 1999 to 2015. The models were combined in a Bayesian framework. We estimated the median true BSE prevalence between 3.74 and 0.216 cases per 100,000 animals for the birth cohorts 1990 to 2001 and observed a peak for the 1996 birth cohort with a point estimate of 16.41 cases per 100,000 cattle. For birth cohorts ranging from 2002 to 2013, the estimated median prevalence was below one case per 100,000 heads. The calculated confidence in freedom from disease (design prevalence 1 in 100,000) was above 99.5% for the birth cohorts 2002 to 2006. In conclusion, BSE surveillance in the healthy slaughtered cattle chain was extremely sensitive at the time, when BSE repeatedly occurred in Germany (2000-2009), because the entry of BSE-infected cattle into the food chain could virtually be prevented by the extensive surveillance program during these years and until 2015 (estimated non-detected cases/100.000 [95% credible interval] in 2000, 2009, and 2015 are 0.64 [0.5,0.8], 0.05 [0.01,0.14], and 0.19 [0.05,0.61], respectively).

Community structure of domesticated pigs in livestock facilities.

The social structure of animal groups is considered to have an impact on their health and welfare. This could also be true for animals under commercial conditions, but research in this area has been limited. Pigs for example are known to be very social animals, but information about their grouping behavior is mostly derived from wild boars and a limited number of studies in seminatural and commercial conditions. Specifically under commercial conditions it is still unclear to what extent pig herds organize themselves in subgroups and how such group patterns emerge. To answer these questions, we tracked the positions of about 200 sows inside a barn during ongoing production over a period of five weeks and used these data to construct and analyze the animal contact networks. Our analysis showed a very high contact density and only little variation in the number of other animals that a specific animal is in contact with. Nevertheless, in each week we consistently detected three subgroups inside the barn, which also showed a clear spatial separation. Our results show that even in the high density environment of a commercial pig farm, the behavior of pigs to form differentiated groups is consistent with their behavior under seminatural conditions. Furthermore, our findings also imply that the barn layout could play an important role in the formation of the grouping pattern. These insights could be used to monitor and understand the spread of infectious diseases inside the barn better. In addition, our insights could potentially be used to improve the welfare of pigs.

Comparison of Bayesian and frequentist methods for prevalence estimation under misclassification.

BACKGROUND: Various methods exist for statistical inference about a prevalence that consider misclassifications due to an imperfect diagnostic test. However, traditional methods are known to suffer from truncation of the prevalence estimate and the confidence intervals constructed around the point estimate, as well as from under-performance of the confidence intervals' coverage. METHODS: In this study, we used simulated data sets to validate a Bayesian prevalence estimation method and compare its performance to frequentist methods, i.e. the Rogan-Gladen estimate for prevalence, RGE, in combination with several methods of confidence interval construction. Our performance measures are (i) error distribution of the point estimate against the simulated true prevalence and (ii) coverage and length of the confidence interval, or credible interval in the case of the Bayesian method. RESULTS: Across all data sets, the Bayesian point estimate and the RGE produced similar error distributions with slight advantages of the former over the latter. In addition, the Bayesian estimate did not suffer from the RGE's truncation problem at zero or unity. With respect to coverage performance of the confidence and credible intervals, all of the traditional frequentist methods exhibited strong under-coverage, whereas the Bayesian credible interval as well as a newly developed frequentist method by Lang and Reiczigel performed as desired, with the Bayesian method having a very slight advantage in terms of interval length. CONCLUSION: The Bayesian prevalence estimation method should be prefered over traditional frequentist methods. An acceptable alternative is to combine the Rogan-Gladen point estimate with the Lang-Reiczigel confidence interval.

Quantitative allergenicity risk assessment of food products containing yellow mealworm (Tenebrio molitor).

Insect-based foods are starting to enter the EU market, raising concerns about their safety. Allergic consumers might be exposed to even a greater risk, since insects have proven to trigger allergic symptoms, particularly in patients sensitised to crustaceans. Current legislation does not enforce producers to include insects in the list of allergenic ingredients. Food allergenicity risk assessment (FARA) is still at its infancy, and the debate on the need to define allergen thresholds is open. In this paper, we aimed at applying the concepts of stochastic quantitative FARA to describe present and future scenarios of exposure to foods containing Tenebrio molitor, the yellow mealworm. According to our risk characterisation, mealworm-based food products represent a major risk for individuals allergic to crustaceans to develop symptoms after the consumption of a dose lower than a serving size. Moreover, other allergic consumers might be at risk. A correct labelling of insect containing foods would help safeguarding the health of EU allergic consumers. Quantitatively assessing the risk of allergenicity provides a clear description of the problem, facilitating the decisional process of the risk manager, supporting the implementation of effective allergen management procedures and limiting the phenomenon of uninformative precautionary labelling.

Comparison of lead levels in edible parts of red deer hunted with lead or non-lead ammunition.

Game meat may contain elevated concentrations of lead especially if lead-containing ammunition is used for hunting. Then a health risk is possible for consumer groups with high game meat intake. The lead concentrations in three edible parts (marketable meat from the area close to the wound channel, saddle and haunch) of meat from red deer (Cervus elaphus) between animals hunted either with lead or non­lead ammunition were compared. Furthermore, lead levels in game meat of lead-shot red deer were compared with those of lead-shot roe deer and lead-shot wild boar. Ninety red deer were shot and killed in the context of this study (64 with lead and 26 with non­lead ammunition). Since the lead concentration for a number of the samples was below the limit of detection or the limit of quantification, statistical methods for left-censored data were applied. The median concentrations of lead in game meat did not differ significantly between lead shot and non­lead shot animals. However, when we analyzed the more elevated lead concentrations, they were significantly higher in edible parts of animals shot with lead ammunition than non-lead ammunition. The highest concentrations were found in samples from edible meat from the area close to the wound channel (max 3442 mg Pb/kg), followed by the saddle (max 1.14 mg Pb/kg) and with the lowest levels in the haunch (max 0.09 mg Pb/kg). A comparison of game species revealed that the lead concentration in haunch and saddle of lead shot red deer was higher than in the corresponding samples of lead shot roe deer. Our results have shown that by the use of non-lead ammunition, a significant reduction of the lead concentration especially in edible parts near the wound channel is possible.

Simple changes of individual studies can improve the reproducibility of the biomedical scientific process as a whole.

We developed a new probabilistic model to assess the impact of recommendations rectifying the reproducibility crisis (by publishing both positive and 'negative' results and increasing statistical power) on competing objectives, such as discovering causal relationships, avoiding publishing false positive results, and reducing resource consumption. In contrast to recent publications our model quantifies the impact of each single suggestion not only for an individual study but especially their relation and consequences for the overall scientific process. We can prove that higher-powered experiments can save resources in the overall research process without generating excess false positives. The better the quality of the pre-study information and its exploitation, the more likely this beneficial effect is to occur. Additionally, we quantify the adverse effects of both neglecting good practices in the design and conduct of hypotheses-based research, and the omission of the publication of 'negative' findings. Our contribution is a plea for adherence to or reinforcement of the good scientific practice and publication of 'negative' findings.

Lead content in wild game shot with lead or non-lead ammunition - Does "state of the art consumer health protection" require non-lead ammunition?

The toxicity of lead has been known for a long time, and no safe uptake level can be derived for humans. Consumers' intake via food should therefore be kept as low as possible. Game meat can contain elevated levels of lead due to the use of lead ammunition for hunting. A risk assessment conducted in 2010 by the German Federal Institute for Risk Assessment including various consumption scenarios revealed a possible health risk for extreme consumers of game meat hunted with lead ammunition (i.e. hunters and members of hunters' households). Babies, infants, children and women of childbearing age were identified as vulnerable group with regards to the developmental neurotoxicity of lead. It was noted, that a sound data base was required in order to refine the assessment. Therefore, the research project "Safety of game meat obtained through hunting" (LEMISI) has been conducted in Germany, with the aims of determining the concentrations of lead (as well as of copper and zinc) brought into the edible parts of game meat (roe deer (Capreolus capreolus) and wild boar (Sus scrofa)) due to using either lead or non-lead hunting ammunition, whilst concurrently taking geogenic (i.e. "background") levels of lead into account. Compared to non-lead ammunition, lead ammunition significantly increased lead concentrations in the game meat. The use of both lead and non-lead ammunition deposited copper and zinc in the edible parts of game meat, and the concentrations were in the range of those detected regularly in meat of farm animals. For the average consumer of game meat in Germany the additional uptake of lead only makes a minor contribution to the average alimentary lead exposure. However, for consumers from hunters' households the resulting uptake of lead-due to lead ammunition-can be several times higher than the average alimentary lead exposure. Non-lead bullets in combination with suitable game meat hygienic measures are therefore recommended in order to ensure "state of the art consumer health protection".

Hunting of roe deer and wild boar in Germany: Is non-lead ammunition suitable for hunting?

BACKGROUND: Non-lead hunting ammunition is an alternative to bullets that contain lead. The use of lead ammunition can result in severe contamination of game meat, thus posing a health risk to consumers. With any kind of ammunition for hunting, the terminal effectiveness of bullets is an animal welfare issue. Doubts about the effectiveness of non-lead bullets for a humane kill of game animals in hunting have been discussed. The length of the escape distance after the shot has been used previously as an indicator for bullet performance. OBJECTIVE: The object of this study was to determine how the bullet material (lead or non-lead) influences the observed escape distances. METHODS: 1,234 records of the shooting of roe deer (Capreolus capreolus) and 825 records of the shooting of wild boar (Sus scrofa) were evaluated. As the bullet material cannot be regarded as the sole cause of variability of escape distances, interactions of other potential influencing variables like shot placement, shooting distance, were analyzed using conditional regression trees and two-part hurdle models. RESULTS: The length of the escape distance is not influenced by the use of lead or non-lead ammunition with either roe deer or wild boar. With roe deer, the length of the escape distance is influenced significantly by the shot placement and the type of hunting. Increasing shooting distances increased the length of the escape distance. With wild boar, shot placement and the age of the animals were found to be a significant influencing factor on the length of the escape distance. CONCLUSIONS: The length of the escape distance can be used as an indicator for adequate bullet effectiveness for humane killings of game animals in hunting.Non-lead bullets already exist which have an equally reliable killing effect as lead bullets.

Copper and zinc content in wild game shot with lead or non-lead ammunition - implications for consumer health protection.

The aim of this study was to examine the contamination of game meat with copper and zinc and establish whether the use of alternative (non-lead) ammunition can lead to higher or unsafe levels of copper and zinc in the meat of roe deer, wild boar and red deer. The research project "Safety of game meat obtained through hunting" (LEMISI) was conducted in Germany with the purpose of examining the entry of lead as well as copper and zinc into the meat of hunted game when using either lead or non-lead ammunition. The outcome of this study shows that the usage of both lead-based ammunition and alternative non-lead ammunition results in the entry of copper and zinc into the edible parts of the game. Using non-lead ammunition does not entail dangerously elevated levels of copper and zinc, so replacing lead ammunition with alternative ammunition does not introduce a further health problem with regard to these metals. The levels of copper and zinc in game meat found in this study are in the range found in previous studies of game. The content of copper and zinc in game meat is also comparable to those regularly detected in meat and its products from livestock (pig, cattle, sheep) for which the mean human consumption rate is much higher. From the viewpoint of consumer health protection, the use of non-lead ammunition does not pose an additional hazard through copper and zinc contamination. A health risk due to the presence of copper and zinc in game meat at typical levels of consumer exposure is unlikely for both types of ammunition.

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

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.

Disease Spread through Animal Movements: A Static and Temporal Network Analysis of Pig Trade in Germany.

BACKGROUND: Animal trade plays an important role for the spread of infectious diseases in livestock populations. The central question of this work is how infectious diseases can potentially spread via trade in such a livestock population. We address this question by analyzing the underlying network of animal movements. In particular, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. METHODOLOGY: 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: 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 do 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.

Spatio-temporal analysis of fox rabies cases in Germany 2005-2006.

Aiming to achieve new insights into rabies dynamics, this paper is the first to investigate fox rabies in Germany from a space-time pattern perspective. Based on a locally restricted dataset covering a fourteen month period, our findings indicate a strongly aggregated spatiotemporal point pattern resulting from an inhomogeneous stochastic process. In contrast to spatial or temporal approaches or cellular automata, our analysis focuses on the disease dynamics in time and space in a continuous time domain. Our findings confirm existing theories regarding fox rabies control highlighting the potential risk of urban areas and the need for effective rabies vaccination.

Cross-neutralization of antibodies induced by vaccination with Purified Chick Embryo Cell Vaccine (PCECV) against different Lyssavirus species.

BACKGROUND: Rabies is a neglected zoonotic disease caused by viruses belonging to the genus lyssavirus. In endemic countries of Asia and Africa, where the majority of the estimated 60,000 human rabies deaths occur, it is mainly caused by the classical rabies virus (RABV) transmitted by dogs. Over the last decade new species within the genus lyssavirus have been identified. Meanwhile 15 (proposed or classified) species exist, including Australian bat lyssavirus (ABLV), European bat lyssavirus (EBLV-1 and -2), Duvenhage virus (DUVV), as well as Lagos bat virus (LBV) and Mokola virus (MOKV) and recently identified novel species like Bokeloh bat lyssavirus (BBLV), Ikoma bat lyssavirus (IKOV) or Lleida bat lyssavirus (LLBV). The majority of these lyssavirus species are found in bat reservoirs and some have caused human infection and deaths. Previous work has demonstrated that Purified Chick Embryo Cell Rabies Vaccine (PCECV) not only induces immune responses against classical RABV, but also elicits cross-neutralizing antibodies against ABLV, EBLV-1 and EBLV-2. MATERIAL & METHODS: Using the same serum samples as in our previous study, this study extension investigated cross-neutralizing activities of serum antibodies measured by rapid fluorescent focus inhibition test (RFFIT) against selected other non-classical lyssavirus species of interest, namely DUVV and BBLV, as well as MOKV and LBV. RESULTS: Antibodies developed after vaccination with PCECV have neutralizing capability against BBLV and DUVV in the same range as against ABLV and EBLV-1 and -2. As expected, for the phylogenetically more distant species LBV no cross-neutralizing activity was found. Interestingly, 15 of 94 serum samples (16%) with a positive neutralizing antibody titer against RABV displayed specific cross-neutralizing activity (65-fold lower than against RABV) against one specific MOKV strain (Ethiopia isolate), which was not seen against a different strain (Nigeria isolate). CONCLUSION: Cross-neutralizing activities partly correlate with the phylogenetic distance of the virus species. Cross-neutralizing activities against the species BBLV and DUVV of phylogroup 1 were demonstrated, in line with previous results of cross-neutralizing activities against ABLV and EBLV-1 and -2. Potential partial cross-neutralizing activities against more distant lyssavirus species like selected MOKV strains need further research.

The impact of zoonotic MRSA colonization and infection in Germany.

Methicillin-resistant Staphylococcus aureus (MRSA) causes colonization and infection both in animals and humans. In Germany, cases of MRSA colonization among humans, w+hich affect 0.5-1.5% of the general population and 1.0-2.5% of patients at hospital admission, are still mostly associated with previous healthcare contact and defined epidemic clonal lineages. However, MRSA is also distributed in livestock production in Germany, mostly without causing infections in the animals. These MRSA predominantly belong to the clonal complex (CC) 398, but also to CC9 and CC97. Zoonotic transmission of MRSA CC398 from livestock to humans occurs predominantly in people with occupational livestock contact. Spread of MRSA CC398 to household members of these persons is also frequently observed, but dissemination in the general population is limited so far However, especially in areas with intensive livestock husbandry, about 20-38% of MRSA CC398 cases among humans cannot be epidemiologically linked to direct livestock contact, indicating other transmission pathways. MRSA CC398 currently causes about 2% of all human MRSA infections (wound infections, pneumonia, sepsis) in Germany, but up to 10% in regions characterized by a high density of livestock-farming. The burden of MRSA in companion animals was demonstrated to range between 3.6-9.4% within wound samples obtained from dogs, cats and horses, respectively. In contrast to livestock and horses, MRSA distributed in pet animals are mostly associated with MRSA clonal lineages that are also prevalent in human healthcare facilities. Overall, zoonotic exchange of MRSA between humans and animals has relevant impact on the epidemiology of MRSA in Germany.

The elimination of fox rabies from Europe: determinants of success and lessons for the future.

Despite perceived challenges to controlling an infectious disease in wildlife, oral rabies vaccination (ORV) of foxes has proved a remarkably successful tool and a prime example of a sophisticated strategy to eliminate disease from wildlife reservoirs. During the past three decades, the implementation of ORV programmes in 24 countries has led to the elimination of fox-mediated rabies from vast areas of Western and Central Europe. In this study, we evaluated the efficiency of 22 European ORV programmes between 1978 and 2010. During this period an area of almost 1.9 million km² was targeted at least once with vaccine baits, with control taking between 5 and 26 years depending upon the country. We examined factors influencing effort required both to control and eliminate fox rabies as well as cost-related issues of these programmes. The proportion of land area ever affected by rabies and an index capturing the size and overlap of successive ORV campaigns were identified as factors having statistically significant effects on the number of campaigns required to both control and eliminate rabies. Repeat comprehensive campaigns that are wholly overlapping much more rapidly eliminate infection and are less costly in the long term. Disproportionally greater effort is required in the final phase of an ORV programme, with a median of 11 additional campaigns required to eliminate disease once incidence has been reduced by 90 per cent. If successive ORV campaigns span the entire affected area, rabies will be eliminated more rapidly than if campaigns are implemented in a less comprehensive manner, therefore reducing ORV expenditure in the longer term. These findings should help improve the planning and implementation of ORV programmes, and facilitate future decision-making by veterinary authorities and policy-makers.

Case-control study on the risks of BSE infections in Northern Germany.

This study was to identify risk factors for bovine spongiform encephalopathy (BSE) by means of individual case-control data. 43 BSE cases in a defined region in Lower Saxony and Schleswig-Holstein were compared with 84 control animals. Purchase of new breeding stock and cross contamination between feed on the farm did not seem to have influence on the BSE incidence in these regions. The results indicate independent risk patterns. Pattern 1: Cows with high milk yield seemed to be at risk on big farms with adjacent pig production and when they were not fed milk replacer. Pattern 2: Milk replacer (esp. from certain producers) is a risk factor for Non-Red Holstein cattle, low yielding cows and farms without pig production. Pattern 3: Red Holstein cattle not being fed milk replacer have a higher BSE risk than other breeds when they have a low milk yield and live on small farms with pig production. This study, like findings in Bavaria, Lower Saxony and Schleswig-Holstein, strengthens the hypothesis that BSE in Germany was caused by a feed mediated ubiquitous exposure to PrP(sc) during a confined time period. Producers, in need of buying animal derived feed components during that time slot, were more likely to spread the PrP(sc) than others. Their increased risk is not necessarily due to an inadequate purchasing policy, but can also be coincidental. The breed Red Holstein is not the risk factor itself but represents the risk from concentrated feed for animals during a susceptible age period (calves). Therefore, the authors suggest a continuous exclusion of animal-derived fat components from milk replacers.

Coherence of animal health, welfare and carcass quality in pork production chains.

Aim of the study was to measure the potential impact of animal health and welfare on the carcass quality. 99 pigs under equal housing and feeding conditions were involved in the study. Effects of the immune system on carcass composition, meat quality and performance data of slaughter pigs became measureable by quantification of acute phase proteins (APP), haptoglobin (Hp) and pig major acute phase protein (Pig-MAP). The results were not significantly affected by gender or breed. The calculated correlations between chosen animal health indicators and carcass quality parameters prove an influence of health and welfare on performance, carcass composition and meat quality traits. The acute phase proteins could also be valuable as a predictive indicator for risk assessment in meat inspection, as increased Hp concentrations in slaughter blood indicate a 16 times higher risk for organ abnormalities and Pig-MAP concentrations above 0.7mg/ml a 10 times higher risk.

On the robustness of in- and out-components in a temporal network.

BACKGROUND: Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time. The first measurements of such networks are very recent so that a profound theoretical understanding is still lacking. In this work, we focus on the propagation properties of infectious diseases in time-dependent networks. In particular, we analyze a dataset containing livestock trade movements. The corresponding networks are known to be a major route for the spread of animal diseases. In this context chronology is crucial. A disease can only spread if the temporal sequence of trade contacts forms a chain of causality. Therefore, the identification of relevant nodes under time-varying network topologies is of great interest for the implementation of counteractions. METHODOLOGY/FINDINGS: We find that a time-aggregated approach might fail to identify epidemiologically relevant nodes. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures. Both measures are refined to gain full awareness of the time-dependent topology and finite infectious periods. We show that the size of the components exhibit strong temporal heterogeneities. In particular, we find that the size of the components is overestimated in time-aggregated networks. For disease control, however, a risk assessment independent of time and specific disease properties is usually favored. We therefore explore the disease parameter range, in which a time-independent identification of central nodes remains possible. CONCLUSIONS: We find a ranking of nodes according to their component sizes reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control.

Unfolding accessibility provides a macroscopic approach to temporal networks.

An accessibility graph of a network contains a link wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding paths of growing length (unfolding), we obtain information about the distribution of shortest path durations and characteristic time scales in temporal networks. Moreover, we define causal fidelity to measure the goodness of their static representation. The practicability of our proposed methods is demonstrated for three examples: networks of social contacts, livestock trade, and sexual contacts.

Spread of infectious diseases in directed and modular metapopulation networks.

We consider epidemics in metapopulations on different network topologies. Recent work on epidemics on networks has focused on epidemics of humans. In this work we present a model for epidemics on directed networks, which are found, for example, in the livestock trade. We show that the direction of edges and the modular structure of networks have an impact on the outbreak size and the time of the outbreak peak. In some circumstances, the outbreak size in directed networks can even be larger than in undirected systems. The results presented here could be useful for decision-making processes in directed modular systems.