conventional methods for studying infectious disease dynamics include a repertoire of modeling techniques :   traditional mean field ( or susceptible - infected - recovered ( sir ) compartmental ) , metapopulation , lattice - based , reaction - diffusion , and network models . the contact network approach , originally developed for applications in the field of statistical physics , has only recently gained in popularity . in network terminology , individuals , or groups of individuals , are defined as nodes , connections between those nodes are edges , and the number of edges from one node to another is the degree ( figure 1 ) . in network epidemiology , a very appealing property of networks is their ability to easily depict the complexity of the real world . in particular , the degree distribution captures heterogeneity in transmission among hosts , allowing the disproportionate role of highly connected individuals networks also often include lists of attributes to nodes or edges that describe between - edge variation in disease transmission or between - host variation in infectiveness or pathogen excretion patterns . in fact , most alternative models can be considered as particular cases of network model . for example , modeling an epidemic using an sir compartmental model is equivalent to using a complete network model in which all the nodes are connected to each other ( figure 2(a ) ) . a lattice - based model can also be replaced by a network model in which nodes that are neighbors on the lattice are connected to each other and all nodes have same degree . because it offers more flexibility , the network approach can be used to answer new questions and to improve disease control . since all individuals and all potential transmission paths are represented in the network , it becomes possible to identify individuals or edges that play a key role for disease transmission . epidemiologists can then propose measures to alter the network in order to prevent or stop disease percolation . for example , vaccinating super - spreading individuals changes the degree distribution , which may be a more efficient way to achieve herd immunity than random vaccination . for these reasons , network techniques have been increasingly used for the study of human diseases     [ 2 , 7 , 8 ] . to obtain parameters for these contact network models , populations of humans can rather easily self - report contact data quickly and efficiently through contact tracing or contact diaries ; there are also clever ways of using proxies for human disease incidence , such as mining the number of flu - related internet queries   or using mobile phone locations as a proxy for human movement or contact - tracing studies .   despite the advantages over traditional disease models , networks are still underused for the study of diseases in wild animal populations . in this paper we describe the state of the art for wildlife network modeling , discuss reasons why network models are an underused tool in wildlife epidemiology , and suggest how contact network epidemiology could become more widespread for biologists . for clarity , we restrict our discussion to microparasites with simple life cycles and focus on between - host disease dynamics . we first present the main reasons why network models are particularly suited to wildlife epidemiology . we then expose a critical particularity of wildlife epidemiology : the type of data that are collected . traditional compartmental or metapopulation epidemiological models assume that individuals constituting an epidemiological system can be pooled in a small number of functional groups within which the disease incidence rate is simply proportional to the number of susceptible and infectious individuals . these models are often qualified as  mass - action models  . within these functional groups , all the individuals are therefore assumed to be epidemiologically identical . the originality of network models resides in their ability to take into account interindividual or intergroup ( i.e. , internode ) variations in epidemiological properties ( e.g. , degree , infectiveness , recovery rate ) . with this high resolution , since network models capture more heterogeneity among nodes than traditional models , fitted network models can be used to predict the impact of interventions targeting individuals that are critical for disease percolation . for example , when the degree distribution is strongly right - skewed , the small number of individuals with the highest degree values tend to be infected very early during the epidemic , and subsequently redistribute the disease to a large number of individuals . these  hub  individuals are then responsible for very high incidence rates at the beginning of the epidemic , which traditional models are unable to predict ( see figure 2 ) . if a mass - action model is used to fit prevalence data collected during this epidemic , the associated goodness - of - fit will be poor , and the estimates of epidemiological parameters will be biased . as explained below , wild animal populations are typical examples of heterogeneous systems and therefore greatly benefit from the network approach .    from the epidemiological point of view , wildlife systems differ in four important respects from human systems : ( i ) the underlying structure of the population , ( ii ) the tools available to collect data on the network structure , ( iii ) available epidemiological data , and ( iv ) potential control options . first , wild animal populations are often highly structured . numerous species live in groups , which generally interact nonrandomly . and within a given area it can be decomposed into elements corresponding to the different observation scales : within - group networks ( level n = 1 ) , between - group networks ( n = 2 ) , and sometimes higher order level networks like between - species network ( n = 3 ) . level - n networks ( with n  2 ) can then be considered as metanetworks , that is , networks of networks , with the networks of the level n-1 constituting the nodes of the level n ( figure 1 ) . wildlife epidemiologists need to estimate basic structural parameters of their study population in order to know how these different networks are combined together . basically they need to answer the following questions : do the animals live in groups ? if so , what is the group size distribution ? how do individuals interact within a group ? are there other potentially relevant hierarchical levels , such as subgroups ( groups inside groups ) or subpopulations ( groups of groups ) ? second , wildlife biologists face multiple challenges when collecting contact data     [ 1214 ] .   behavioral observations of animals rarely allow inferring exact , full contact networks , as it is basically impossible to watch all individuals of a population at the same time . the use of indirect measures ( through technology ) can help this problem , although the number of individuals that can be simultaneously monitored is often limited due to logistical difficulties or the high costs of technology ( but see   which might have recorded a full network of a study lizard population ) .   more commonly , a representative subset of the study population is generally chosen and then either directly observed using standard behavioral sampling methods or indirectly monitored using biologgers , radio telemetry , mark - recapture , or other methods ( for a discussion of methods see table 1 ) . when choosing a technique to inform a contact model , it is important to take into account whether the species is habituated or not , captive or wild , the local environment of the population ( e.g. , heavily forested or underwater ) , the size of the animal , the resolution of the data needed to create a contact network specific to that animal 's behavior , the budget , and the sample size needed . it is important not to change the animal 's behavior using these techniques , for example through observer presence of timid animals , or heavy tags limiting movement . ( i ) contact networks are normally derived from healthy individuals , and an animal 's behavior , and hence the topography of the contact network , might change upon infection . often it is unknown whether infection would alter the network structure by causing more contacts ( e.g. ,  furious rabies ) or fewer contacts (  dumb  rabies ) .   in this case , a sensitivity analysis could be used to hedge against any changes in contact rates due to infection . ( ii ) it is quite difficult to define a  contact  ; clearly the definition of a contact will depend on the transmission of the pathogen of interest . the best way to get answers to these questions is to do controlled transmission experiments , but this can be ethically challenging , especially for wild animals of conservation concern . ( iii ) once a definition of  contact  is created , and a technique chosen to capture these contacts , it is then difficult to measure other types of social interactions for which you are not monitoring . ( iv ) despite the recent technological advances allowing the collection of biologically relevant contact data for the majority of a population , how to sample a network is still a problem . for example , technological failures can lead to incomplete networks even if the whole population was successfully tagged , and there are often edge effects with other populations . ( v ) the type of method used to collect the contact data can influence the properties of the network , hence the infectious period of the disease must be taken into account when choosing a method .   because another behavioral variable is normally being used as a proxy for contact ( i.e. , proximity data ) , the raw data collected from these indirect measures does not immediately yield a contact network . but , after adequate processing , it becomes possible to reconstruct contact networks that will not exactly match the actual full network , but will rather have the same statistical , and hence epidemiological , properties . wild animal contact networks also often , if not always , exhibit temporal variation , creating a dynamic network . for example , individuals or groups can migrate to a different area ( e.g. , reindeer , wildebeest , birds , monarch butterflies ) , individuals can transfer to a different group ( e.g. , ) , and animal societies can fission - fusion ( e.g. , hyenas , chimpanzees , bottlenose dolphins , elephants , lions , and guppies ) . in addition , contact networks can change over long time scales due to demographic processes such as births and deaths . theoretical studies have shown that the spread of infectious diseases in dynamic networks differs from static networks . significant changes in contact patterns during the course of an epidemic need to be accounted for , and this data describing contact network dynamics can be obtained using direct observation or technology as listed above and in table 1 . incidence can be recorded through passive surveillance operations or direct observation for only the few diseases where wild animals exhibit overt clinical signs ( e.g. , rabies     ) . however , the majority of wild animals do not show visual signs of disease and most wild animals simply disappear when they die . in the field it is often difficult to detect carcasses , and more worrying , even detect any sort of die - off ( e.g. , ) . as another example , out of over 1000 lions suspected to die in a fatal canine distemper virus outbreak in the serengeti in 1994 , only 11 carcasses were recovered from a highly - monitored population . blood can be screened directly for pathogens or indirectly for antibodies to pathogens to provide insight on disease dynamics . longitudinal surveys are generally the preferred type of serological survey ; cross - sectional serological surveys can be misleading because antibodies persist long after the end of the infection . collecting blood samples is only possible if the study animals can be trapped or darted . it is generally expensive , time - consuming , and potentially risky to the animal . however , in recent years , noninvasive disease screening methods have been developed , such as immunoglobulin dosage in urine and feces ( e.g. , siv in chimps ) or parasite genotyping in feces ( e.g. , malaria in great apes     ) . human outbreaks often involve animals , but generally only at the very beginning ; whereas in wildlife , multiple species are often involved during the entire course of the outbreak . this increases the complexity of building a multihost network , and often it is challenging to have accurate assessments of contact networks from multiple hosts , forcing a fall - back strategy on mean field models . finally , despite constraints to inferring the structure of the contact network and collecting disease data , network models allow us to easily evaluate a wide range of disease control interventions in wildlife populations . in humans , because there are numerous ways to modify human networks , such as school closure , travel warnings , and airport closure in certain cases , public health actions often focus on improving epidemiological surveillance and implementing subsequent vaccination campaigns . in wildlife epidemiology , parenteral vaccination can be used for small wild animal populations , but is logistically challenging and sometimes considered too invasive . wildlife contact networks can also be modified by reducing contacts between domestic animals , humans , and wildlife to avoid the spillover to wildlife in the first place  this is a type of quarantine     [ 6466 ] . population density can also be reduced through culling or decreasing birth rates     [ 34 , 67 ] . an important benefit of the network approach is the ability to identify central individuals likely responsible for most transmission events . when those individuals are targeted for intervention purposes , this reduces the number of wildlife needing to be culled or vaccinated , for example . in the past 510 years , wildlife biologists have made solid progress in characterizing contact networks in wildlife populations . through the use of these contact networks for example , superspreading animals have been found in some populations ( e.g. , deer mice and possums [ 23 , 28 ] ) , while they are not obvious in other systems ( e.g. , tasmanian devil and african lion populations     [ 4 , 24 ] ) . the tasmanian devil network was found to be one giant component , meaning that the whole endangered population is threatened by a novel infectious cancer . well - connected individuals were more likely to be infected in some wildlife populations ( brushtail possums , sleepy lizards , skinks , and bumble - bees     [ 15 , 29 , 32 , 39 ] ) but not in others ( meerkats ) . in a study of possums , in contrast , abundance thresholds above which disease can spread ( percolation thresholds ) have been identified in gerbils with plague   and in multihost plague systems of mice and prairie dogs . with networks , temporal changes in contact patterns were also identified as critical for the spread of respiratory diseases in wild chimpanzees . issues of different spatial scales have been tackled with networks , specifically the relative importance of local versus long range transmission events in driving disease spread . finally , multilevel network models have been developed and successfully applied to tuberculosis transmission between badgers groups and cows . for a more extensive list of insights we refer to table 1 of a recent review networks have been used in other fields like statistical physics for decades , yet have only in the past 10 years really taken off with the human epidemiology literature , and are now at the cutting edge of wildlife epidemiology . the number of studies using this approach is still relatively limited , but of those studies combining networks and wildlife , they often get published in high profile journals  potentially indicating that wildlife network epidemiology is still in its infancy . second , the network literature , especially in the physics literature , is quite hard to grasp and at first sight , may seem complicated for the field biologist . the analytical treatment of network epidemiological models is however only slightly more difficult than solving systems of differential equations of mass action models . a few articles are notable for presenting the mathematics of network models in an accessible way for biologists     [ 7274 ] . however , finding analytical solutions is not always necessary . agent - based stochastic simulations can be good alternatives and are relatively easy to implement . they are particularly interesting to model complex systems that have a lot of parameters and hence can not be described by closed form equations . unfortunately there is limited network software with easy - to - use graphical user interfaces implementing these methods , and often people program their own network simulation models ( table 2 ) . coding using basic programming languages ( e.g. , r , python or netlogo ) is often a disparate skill set from a field biologist who successfully collects contact and epidemiological data on wild populations . third , networks are indeed data intensive , and wildlife systems are unfortunately often data limited . for example , in constructing a contact network for a population of serengeti lions , only 36 pride - to - pride contacts were observed per 1294 hours of daylight observation over a 3 year time period . in addition , wild animals can not be continuously observed , and dealing with gaps and missing data is often challenging ( see section 4 ) . finally , contact networks are inferred from contact data collected for a specific species , for a specific ecosystem , and for a specific period of time . therefore it can be difficult to generalize epidemiological results obtained with a network model to other circumstances ( e.g. , ) . wildlife epidemiologists should be encouraged to promote their network approach at meetings and in journals that have not normally embraced a network approach . more training sessions such as sismid ( university of washington ) or insna 's workshops at sunbelt would be useful . a formal comparison between network and mean - field models would also help spread the word . currently , there are few papers comparing the performance of mean - field and network models . although scientists might have tried multiple modeling approaches during the course of the study , normally only one approach is published . well enough ,  but we are unaware of any formal quantitative comparison of the pros and cons of using mean - field versus network models for a range of empirical and theoretical systems . it is likely that network models are only going to get more complex : they will include more parameters and variables . , it is important to note that stochastic agent - based modeling handles very complex models but is generally not complicated . in the last few years , biologists have increasingly used these types of models to investigate respective effects of different variables on biological phenomenon . several software and user - friendly computer languages are particularly suited to develop network epidemiological agent - based models ( table 2 ) . the recent developments in approximate bayesian computation ( abc ) , a set of methods initially developed by population geneticists , greatly facilitate agent - based model fitting     [ 8486 ] . we would like to attract the attention of epidemiologist to these methods , which we believe will be used extensively in the future . technology is helping to bridge the gap between data - intensive network models , and the challenges inherent in collecting contact data . there has been a burst of new technology such as satellite gps radio telemetry , proximity data loggers , camera and video traps , tracking , proximity data radio collars , powder marking , pit tags , and antennae , and capture - mark - recapture ( table 1 ) . ignoring the gaps inherent to these datasets can lead to biased estimates of contact network or epidemiological parameters . for example , if an animal is observed susceptible at time t and reobserved infected 10 days later , should we assume that it became infected on the first day , on the last day , or maybe after five days ? first , survival analyses , that were initially developed to estimate survival rates using date - of - last - observation data can also be applied , for example , to estimate rates of seroconversion . second , multistate capture - mark - recapture ( cmr ) models have proven very useful to estimate animal migration rates , survival rates , and rates of change of individual state ( for example , states s , i or r ) . although user - friendly software exists to fit cmr models ( table 2 ) , these models could be more broadly used in wildlife epidemiology , both to estimate network parameters and epidemiological parameters . third , agent - based models , coupled with abc fitting procedure , can easily circumvent the problem of missing data     [ 8486 ] . our purpose here is to attract the attention of epidemiologists to these methods rather than to describe them in detail , so we encourage interested readers to consult the references cited . an exciting and useful push for future directions would be to develop theoretical advances for network models that allow us to develop understanding these rules , in particular how ecological variables such as food resource distribution , distribution of conspecifics , and climate influence contact patterns , would allow identifying universal principles governing networks ' structure . it would then become possible to extrapolate these mechanistic models to other populations , areas , or time periods . this is even more pertinent to wildlife network epidemiology , because new fields such as behavioral ecology , capture - mark - recapture , and advanced statistics are combined . field biologists know their system , and know how to collect data , while theoreticians can work on the hardcore modeling aspects . importantly , we believe collaborations should take place at all stages of epidemiological studies , from the design of the data collection protocol to the end of the modeling stage . although using this approach requires some substantial training , the learning curve is not as steep as it seems , and several software and interpreted computer languages have been developed that will make this step easier . in any case , we strongly believe that the benefits far outweigh these costs . the number of applications of network models in wildlife epidemiology is already broad , and for example , network models are well - suited to combine network and genetic data , potentially for viral diseases such as feline immunodeficiency virus and simian immunodeficiency virus . contact network epidemiology using directed networks ( where there is stronger transmission in one direction ) has been applied to animals using the same resting spots for indirectly transmitted pathogens [ 15 , 29 ] , and could be expanded to fresh water organisms because river networks are easy to map , have a good spatial component , and pathogens might travel downstream . we feel that developing collaboration between field biologists and network modelers will be a key factor bringing advances to wildlife epidemiology .
although the approach of contact network epidemiology has been increasing in popularity for studying transmission of infectious diseases in human populations , it has generally been an underutilized approach for investigating disease outbreaks in wildlife populations . in this paper 
 we explore the differences between the type of data that can be collected on human and wildlife populations , provide an update on recent advances that have been made in wildlife epidemiology by using a network approach , and discuss why networks might have been underutilized and why networks could and should be used more in the future . 
 we conclude with ideas for future directions and a call for field biologists and network modelers to engage in more cross - disciplinary collaboration .