Disease Surveillance on Complex Social Networks

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors—sampling the most connected, random, and friends of random individuals—in three complex social networks—a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals—early and accurate detection of epidemic emergence and peak, and general situational awareness—we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R₀). For diseases with a low R₀, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R₀ is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information.     

Potential Parasite Transmission in Multi-Host Networks Based on Parasite Sharing

Epidemiological networks are commonly used to explore dynamics of parasite transmission among individuals in a population of a given host species. However, many parasites infect multiple host species, and thus multi-host networks may offer a better framework for investigating parasite dynamics. We investigated the factors that influence parasite sharing – and thus potential transmission pathways – among rodent hosts in Southeast Asia. We focused on differences between networks of a single host species and networks that involve multiple host species. In host-parasite networks, modularity (the extent to which the network is divided into subgroups of rodents that interact with similar parasites) was higher in the multi-species than in the single-species networks. This suggests that phylogeny affects patterns of parasite sharing, which was confirmed in analyses showing that it predicted affiliation of individuals to modules. We then constructed “potential transmission networks” based on the host-parasite networks, in which edges depict the similarity between a pair of individuals in the parasites they share. The centrality of individuals in these networks differed between multi- and single-species networks, with species identity and individual characteristics influencing their position in the networks. Simulations further revealed that parasite dynamics differed between multi- and single-species networks. We conclude that multi-host networks based on parasite sharing can provide new insights into the potential for transmission among hosts in an ecological community. In addition, the factors that determine the nature of parasite sharing (i.e. structure of the host-parasite network) may impact transmission patterns.     

Social Networks and Knowledge Transmission Strategies among Baka Children,Southeastern Cameroon

The dynamics of knowledge transmission and acquisition, or how different aspects of culture are passed from one individual to another and how they are acquired and embodied by individuals, are central to understanding cultural evolution. In small-scale societies, cultural knowledge is largely acquired early in life through observation, imitation, and other forms of social learning embedded in daily experiences. However, little is known about the pathways through which such knowledge is transmitted, especially during middle childhood and adolescence. This study presents new empirical data on cultural knowledge transmission during childhood. Data were collected among the Baka, a forager-farmer society in southeastern Cameroon. We conducted structured interviews with children between 5 and 16 years of age (n?=?58 children; 177 interviews, with children being interviewed 1–6 times) about group composition during subsistence activities. Children’s groups were generally diverse, although children tended to perform subsistence activities primarily without adults and with same-sex companions. Group composition varied from one subsistence activity to another, which suggests that the flow of knowledge might also vary according to the activity performed. Analysis of the social composition of children’s subsistence groups shows that vertical and oblique transmission of subsistence-related knowledge might not be predominant during middle childhood and adolescence. Rather, horizontal transmission appears to be the most common knowledge transmission strategy used by Baka children during middle childhood and adolescence, highlighting the importance of other children in the transmission of knowledge.     

Bioassay Studies Support the Potential for Iatrogenic Transmission of Variant Creutzfeldt Jakob Disease through Dental Procedures

Background

Evidence is required to quantify the potential risks of transmission of variant Creutzfeldt Jakob (vCJD) through dental procedures. Studies, using animal models relevant to vCJD, were performed to address two questions. Firstly, whether oral tissues could become infectious following dietary exposure to BSE? Secondly, would a vCJD-contaminated dental instrument be able to transmit disease to another patient?

Methods

BSE-301V was used as a clinically relevant model for vCJD. VM-mice were challenged by injection of infected brain homogenate into the small intestine (Q1) or by five minute contact between a deliberately-contaminated dental file and the gingival margin (Q2). Ten tissues were collected from groups of challenged mice at three or four weekly intervals, respectively. Each tissue was pooled, homogenised and bioassayed in indicator mice.

Findings

Challenge via the small intestine gave a transmission rate of 100% (mean incubation 157±17 days). Infectivity was found in both dental pulp and the gingival margin within 3 weeks of challenge and was observed in all tissues tested within the oral cavity before the appearance of clinical symptoms. Following exposure to deliberately contaminated dental files, 97% of mice developed clinical disease (mean incubation 234±33 days).

Interpretation

Infectivity was higher than expected, in a wider range of oral tissues, than was allowed for in previous risk assessments. Disease was transmitted following transient exposure of the gingiva to a contaminated dental file. These observations provide evidence that dental procedures could be a route of cross-infection for vCJD and support the enforcement of single-use for certain dental instruments.     

Quantification of Shared Air: A Social and Environmental Determinant of Airborne Disease Transmission

Background

Tuberculosis is endemic in Cape Town, South Africa where a majority of the population become tuberculosis infected before adulthood. While social contact patterns impacting tuberculosis and other respiratory disease spread have been studied, the environmental determinants driving airborne transmission have not been quantified.

Methods

Indoor carbon dioxide levels above outdoor levels reflect the balance of exhaled breath by room occupants and ventilation. We developed a portable monitor to continuously sample carbon dioxide levels, which were combined with social contact diary records to estimate daily rebreathed litres. A pilot study established the practicality of monitor use up to 48-hours. We then estimated the daily volumes of air rebreathed by adolescents living in a crowded township.

Results

One hundred eight daily records were obtained from 63 adolescents aged between 12- and 20-years. Forty-five lived in wooden shacks and 18 in brick-built homes with a median household of 4 members (range 2–9). Mean daily volume of rebreathed air was 120.6 (standard error: 8.0) litres/day, with location contributions from household (48%), school (44%), visited households (4%), transport (0.5%) and other locations (3.4%). Independent predictors of daily rebreathed volumes included household type (p = 0.002), number of household occupants (p = 0.021), number of sleeping space occupants (p = 0.022) and winter season (p<0.001).

Conclusions

We demonstrated the practical measurement of carbon dioxide levels to which individuals are exposed in a sequence of non-steady state indoor environments. A novel metric of rebreathed air volume reflects social and environmental factors associated with airborne infection and can identify locations with high transmission potential.     

Interactions between Social Structure,Demography, and Transmission Determine Disease Persistence in Primates

Catastrophic declines in African great ape populations due to disease outbreaks have been reported in recent years, yet we rarely hear of similar disease impacts for the more solitary Asian great apes, or for smaller primates. We used an age-structured model of different primate social systems to illustrate that interactions between social structure and demography create ‘dynamic constraints’ on the pathogens that can establish and persist in primate host species with different social systems. We showed that this varies by disease transmission mode. Sexually transmitted infections (STIs) require high rates of transmissibility to persist within a primate population. In particular, for a unimale social system, STIs require extremely high rates of transmissibility for persistence, and remain at extremely low prevalence in small primates, but this is less constrained in longer-lived, larger-bodied primates. In contrast, aerosol transmitted infections (ATIs) spread and persist at high prevalence in medium and large primates with moderate transmissibility;, establishment and persistence in small-bodied primates require higher relative rates of transmissibility. Intragroup contact structure – the social network - creates different constraints for different transmission modes, and our model underscores the importance of intragroup contacts on infection prior to intergroup movement in a structured population. When alpha males dominate sexual encounters, the resulting disease transmission dynamics differ from when social interactions are dominated by mother-infant grooming events, for example. This has important repercussions for pathogen spread across populations. Our framework reveals essential social and demographic characteristics of primates that predispose them to different disease risks that will be important for disease management and conservation planning for protected primate populations.     

The Social Life of Infants in the Context of Infectious Disease Transmission; Social Contacts and Mixing Patterns of the Very Young

Insight into how humans interact helps further understanding of the transmission of infectious diseases. For diseases such as pertussis, infants are at particular risk for severe outcomes. To understand the contact pattern of infants, especially those too young to be vaccinated, we sent contact diaries to a representative sample of 1000 mothers in the United Kingdom. We received 115 responses with a total of 758 recorded contacts. The average number of daily contacts for an infant was 6.68 overall and 5.7 for those aged ≤10 weeks. Of the latter, 2.1 (37%) contacts were with non-household members and were >15 minutes duration, suggesting that a cocooning programme may miss a substantial proportion of exposures leading to disease transmission. The least contact was between adolescents and infants. Thus the impact of adolescent (pertussis) vaccination on infants would likely be limited, unless it reduces transmission to other age groups whose contact with infants is greater.     

When More Transmission Equals Less Disease: Reconciling the Disconnect between Disease Hotspots and Parasite Transmission

The assumed straightforward connection between transmission intensity and disease occurrence impacts surveillance and control efforts along with statistical methodology, including parameter inference and niche modeling. Many infectious disease systems have the potential for this connection to be more complicated–although demonstrating this in any given disease system has remained elusive. Hemorrhagic disease (HD) is one of the most important diseases of white-tailed deer and is caused by viruses in the Orbivirus genus. Like many infectious diseases, the probability or severity of disease increases with age (after loss of maternal antibodies) and the probability of disease is lower upon re-infection compared to first infection (based on cross-immunity between virus strains). These broad criteria generate a prediction that disease occurrence is maximized at intermediate levels of transmission intensity. Using published US field data, we first fit a statistical model to predict disease occurrence as a function of seroprevalence (a proxy for transmission intensity), demonstrating that states with intermediate seroprevalence have the highest level of case reporting. We subsequently introduce an independently parameterized mechanistic model supporting the theory that high case reporting should come from areas with intermediate levels of transmission. This is the first rigorous demonstration of this phenomenon and illustrates that variation in transmission rate (e.g. along an ecologically-controlled transmission gradient) can create cryptic refuges for infectious diseases.     

Potential Role for Fish in Transmission of Mycobacterium ulcerans Disease (Buruli Ulcer): an Environmental Study

This study reports a potential role that fish may play in the transmission of Mycobacterium ulcerans disease (Buruli ulcer). Fish found positive for M. ulcerans DNA all appear to feed on insects or plankton and are believed to concentrate M. ulcerans from this usual food source. These observations provide additional data supporting our previous hypothesis on sources of M. ulcerans and modes of transmission.     

Tissue-Specific Functional Networks for Prioritizing Phenotype and Disease Genes

Integrated analyses of functional genomics data have enormous potential for identifying phenotype-associated genes. Tissue-specificity is an important aspect of many genetic diseases, reflecting the potentially different roles of proteins and pathways in diverse cell lineages. Accounting for tissue specificity in global integration of functional genomics data is challenging, as “functionality” and “functional relationships” are often not resolved for specific tissue types. We address this challenge by generating tissue-specific functional networks, which can effectively represent the diversity of protein function for more accurate identification of phenotype-associated genes in the laboratory mouse. Specifically, we created 107 tissue-specific functional relationship networks through integration of genomic data utilizing knowledge of tissue-specific gene expression patterns. Cross-network comparison revealed significantly changed genes enriched for functions related to specific tissue development. We then utilized these tissue-specific networks to predict genes associated with different phenotypes. Our results demonstrate that prediction performance is significantly improved through using the tissue-specific networks as compared to the global functional network. We used a testis-specific functional relationship network to predict genes associated with male fertility and spermatogenesis phenotypes, and experimentally confirmed one top prediction, Mbyl1. We then focused on a less-common genetic disease, ataxia, and identified candidates uniquely predicted by the cerebellum network, which are supported by both literature and experimental evidence. Our systems-level, tissue-specific scheme advances over traditional global integration and analyses and establishes a prototype to address the tissue-specific effects of genetic perturbations, diseases and drugs.     

Mapping Potential Amplification and Transmission Hotspots for MERS-CoV,Kenya

Dromedary camels have been implicated consistently as the source of Middle East respiratory syndrome coronavirus (MERS-CoV) human infections and attention to prevent and control it has focused on camels. To understanding the epidemiological role of camels in the transmission of MERS-CoV, we utilized an iterative empirical process in Geographic Information System (GIS) to identify and qualify potential hotspots for maintenance and circulation of MERS-CoV, and produced risk-based surveillance sites in Kenya. Data on camel population and distribution were used to develop camel density map, while camel farming system was defined using multi-factorial criteria including the agro-ecological zones (AEZs), production and marketing practices. Primary and secondary MERS-CoV seroprevalence data from specific sites were analyzed, and location-based prevalence matching with camel densities was conducted. High-risk convergence points (migration zones, trade routes, camel markets, slaughter slabs) were profiled and frequent cross-border camel movement mapped. Results showed that high camel-dense areas and interaction (markets and migration zones) were potential hotspot for transmission and spread. Cross-border contacts occurred with in-migrated herds at hotspot locations. AEZ differential did not influence risk distribution and plausible risk factors for spatial MERS-CoV hotspots were camel densities, previous cases of MERS-CoV, high seroprevalence and points of camel convergences. Although Kenyan camels are predisposed to MERS-CoV, no shedding is documented to date. These potential hotspots, determined using anthropogenic, system and trade characterizations should guide selection of sampling/surveillance sites, high-risk locations, critical areas for interventions and policy development in Kenya, as well as instigate further virological examination of camels.     

Sheep Movement Networks and the Transmission of Infectious Diseases

Background and Methodology

Various approaches have been used to investigate how properties of farm contact networks impact on the transmission of infectious diseases. The potential for transmission of an infection through a contact network can be evaluated in terms of the basic reproduction number, R ₀. The magnitude of R ₀ is related to the mean contact rate of a host, in this case a farm, and is further influenced by heterogeneities in contact rates of individual hosts. The latter can be evaluated as the second order moments of the contact matrix (variances in contact rates, and co-variance between contacts to and from individual hosts). Here we calculate these quantities for the farms in a country-wide livestock network: >15,000 Scottish sheep farms in each of 4 years from July 2003 to June 2007. The analysis is relevant to endemic and chronic infections with prolonged periods of infectivity of affected animals, and uses different weightings of contacts to address disease scenarios of low, intermediate and high animal-level prevalence.

Principal Findings and Conclusions

Analysis of networks of Scottish farms via sheep movements from July 2003 to June 2007 suggests that heterogeneities in movement patterns (variances and covariances of rates of movement on and off the farms) make a substantial contribution to the potential for the transmission of infectious diseases, quantified as R ₀, within the farm population. A small percentage of farms (<20%) contribute the bulk of the transmission potential (>80%) and these farms could be efficiently targeted by interventions aimed at reducing spread of diseases via animal movement.     

Optimizing Online Social Networks for Information Propagation

Online users nowadays are facing serious information overload problem. In recent years, recommender systems have been widely studied to help people find relevant information. Adaptive social recommendation is one of these systems in which the connections in the online social networks are optimized for the information propagation so that users can receive interesting news or stories from their leaders. Validation of such adaptive social recommendation methods in the literature assumes uniform distribution of users'' activity frequency. In this paper, our empirical analysis shows that the distribution of online users'' activity is actually heterogenous. Accordingly, we propose a more realistic multi-agent model in which users'' activity frequency are drawn from a power-law distribution. We find that previous social recommendation methods lead to serious delay of information propagation since many users are connected to inactive leaders. To solve this problem, we design a new similarity measure which takes into account users'' activity frequencies. With this similarity measure, the average delay is significantly shortened and the recommendation accuracy is largely improved.     

Two-Level Scheduling for Video Transmission over Downlink OFDMA Networks

This paper presents a two-level scheduling scheme for video transmission over downlink orthogonal frequency-division multiple access (OFDMA) networks. It aims to maximize the aggregate quality of the video users subject to the playback delay and resource constraints, by exploiting the multiuser diversity and the video characteristics. The upper level schedules the transmission of video packets among multiple users based on an overall target bit-error-rate (BER), the importance level of packet and resource consumption efficiency factor. Instead, the lower level renders unequal error protection (UEP) in terms of target BER among the scheduled packets by solving a weighted sum distortion minimization problem, where each user weight reflects the total importance level of the packets that has been scheduled for that user. Frequency-selective power is then water-filled over all the assigned subcarriers in order to leverage the potential channel coding gain. Realistic simulation results demonstrate that the proposed scheme significantly outperforms the state-of-the-art scheduling scheme by up to 6.8 dB in terms of peak-signal-to-noise-ratio (PSNR). Further test evaluates the suitability of equal power allocation which is the common assumption in the literature.     

Temporal Variability and Social Heterogeneity in Disease Transmission: The Case of SARS in Hong Kong

The extent to which self-adopted or intervention-related changes in behaviors affect the course of epidemics remains a key issue for outbreak control. This study attempted to quantify the effect of such changes on the risk of infection in different settings, i.e., the community and hospitals. The 2002–2003 severe acute respiratory syndrome (SARS) outbreak in Hong Kong, where 27% of cases were healthcare workers, was used as an example. A stochastic compartmental SEIR (susceptible-exposed-infectious-removed) model was used: the population was split into healthcare workers, hospitalized people and general population. Super spreading events (SSEs) were taken into account in the model. The temporal evolutions of the daily effective contact rates in the community and hospitals were modeled with smooth functions. Data augmentation techniques and Markov chain Monte Carlo (MCMC) methods were applied to estimate SARS epidemiological parameters. In particular, estimates of daily reproduction numbers were provided for each subpopulation. The average duration of the SARS infectious period was estimated to be 9.3 days (±0.3 days). The model was able to disentangle the impact of the two SSEs from background transmission rates. The effective contact rates, which were estimated on a daily basis, decreased with time, reaching zero inside hospitals. This observation suggests that public health measures and possible changes in individual behaviors effectively reduced transmission, especially in hospitals. The temporal patterns of reproduction numbers were similar for healthcare workers and the general population, indicating that on average, an infectious healthcare worker did not infect more people than any other infectious person. We provide a general method to estimate time dependence of parameters in structured epidemic models, which enables investigation of the impact of control measures and behavioral changes in different settings.     

A Model for Chagas Disease with Oral and Congenital Transmission

This work presents a new mathematical model for the domestic transmission of Chagas disease, a parasitic disease affecting humans and other mammals throughout Central and South America. The model takes into account congenital transmission in both humans and domestic mammals as well as oral transmission in domestic mammals. The model has time-dependent coefficients to account for seasonality and consists of four nonlinear differential equations, one of which has a delay, for the populations of vectors, infected vectors, infected humans, and infected mammals in the domestic setting. Computer simulations show that congenital transmission has a modest effect on infection while oral transmission in domestic mammals substantially contributes to the spread of the disease. In particular, oral transmission provides an alternative to vector biting as an infection route for the domestic mammals, who are key to the infection cycle. This may lead to high infection rates in domestic mammals even when the vectors have a low preference for biting them, and ultimately results in high infection levels in humans.     

Transmission Networks and Population Turnover of Echovirus 30

Globally, echovirus 30 (E30) is one of the most frequently identified enteroviruses and a major cause of meningitis. Despite its wide distribution, little is known about its transmission networks or the dynamics of its recombination and geographical spread. To address this, we have conducted an extensive molecular epidemiology and evolutionary study of E30 isolates collected over 8 years from a geographically wide sample base (11 European countries, Asia, and Australia). 3Dpol sequences fell into several distinct phylogenetic groups, interspersed with other species B serotypes, enabling E30 isolates to be classified into 38 recombinant forms (RFs). Substitutions in VP1 and 3Dpol regions occurred predominantly at synonymous sites (ratio of nonsynonymous to synonymous substitutions, 0.05) with VP1 showing a rapid substitution rate of 8.3 × 10⁻³ substitutions per site per year. Recombination frequency was tightly correlated with VP1 divergence; viruses differing by evolutionary distances of >0.1 (or 6 years divergent evolution) almost invariably (>97%) had different 3Dpol groups. Frequencies of shared 3Dpol groups additionally correlated with geographical distances, with Europe and South Asia showing turnover of entirely distinct virus populations. Population turnover of E30 was characterized by repeated cycles of emergence, dominance, and disappearance of individual RFs over periods of 3 to 5 years, although the existence and nature of evolutionary selection underlying these population replacements remain unclear. The occurrence of frequent “sporadic” recombinants embedded within VP1 groupings of other RFs and the much greater number of 3Dpol groups than separately identifiable VP1 lineages suggest frequent recombination with an external diverse reservoir of non-E30 viruses.The genus Enterovirus in the family Picornaviridae is a group of nonenveloped RNA viruses that cause a wide range of diseases in humans and other mammals. Enteroviruses contain a positive-sense RNA genome of approximately 7,500 nucleotides encoding a polyprotein that after cleavage yields structural (capsid proteins VP1 to VP4) and nonstructural (2A to 3D) proteins. Primary infection with an enterovirus leads to viral replication in the tissue around the gastrointestinal tract, followed by a transient viremia and sometimes migration into other tissues (6, 44). Although infection in immunocompetent individuals is often asymptomatic or causes mild febrile illness, enteroviruses are a common etiological agent in aseptic meningitis, encephalitis, and paralysis in individuals of all ages, with persistent and/or widely disseminated systemic infection in immunosuppressed individuals and neonates (12, 19, 23).Enteroviruses were originally classified as polioviruses, coxsackie virus type A or B viruses, or echoviruses (enteric cytopathic human orphan viruses), depending upon the infectious properties of the virus such as pathogenicity in mice (reviewed in reference 22). From the 1960s onwards, enteroviruses within these groups were further differentiated into serotypes originally by using panels of specific neutralizing antisera and, more recently, by sequence comparisons of structural gene regions such as VP1 (9, 34, 38, 43). There are currently over 100 recognized human enterovirus serotypes that fall into four main species (designated A to D) using phylogenetic analysis (54). The Enterovirus genus additionally contains several other species infecting primates, cattle, and pigs and has recently been expanded to include the genetically related human rhinovirus A and B (54).The species B serotype, echovirus 30 (E30), is a major cause of meningitis in both children and adults. Among the many serotypes associated with this disease presentation, E30 is generally the most commonly isolated in Europe (8, 31, 49), the United States (10, 37), Asia (1, 60), and South America (33). E30 infections typically occur as a series of outbreaks every 3 to 5 years, frequently over large geographical areas. For example, high frequencies of E30 detection in meningitis cases and surveillance programs were reported for 2000 to 2001 throughout Europe, including Denmark (58), Belgium (57), Cyprus (45), Germany (46), and France (3, 5), and again in 2005 to 2006 (8). Similarly, in the United States, long-term surveillance by the Centers for Disease Control and Prevention revealed peaks of E30 isolation in 1981, 1991 to 1993, 1997, and 2003 (10, 37). The underlying basis for this periodicity in E30 infections and the possible association of different genetic variants of E30 with outbreaks are currently poorly understood.At any one time point, a range of different species B enterovirus serotypes circulate in human populations. The evolution of enteroviruses occurs through genetic drift and, over much longer periods, antigenic diversification in the structural gene region encoding the virus capsid (7, 14, 25, 30, 51, 55); it may also occur by recombination between the capsid and nonstructural coding parts of the genome and the 5′ untranslated region (2, 13, 16, 20, 26, 28, 29, 35, 39, 41, 47, 48, 53). To date, almost all documented examples of recombination have been limited to members of the same species (e.g., between species B serotypes), with the exception of the 5′ untranslated region, where only a single genetic group can be identified within human species A and B and a second with species C and D (48).In this study, we have carried out an extensive investigation of VP1 sequence divergence and recombination through sequencing the 3Dpol region of E30 isolates and samples collected from several European countries, Southeast Asia, and Australia over a combined 8-year observation period. Using this geographically diverse sample collection, our aims were to document the time span and geographical extent of different E30 variants as they emerged and spread during the observation period. The identification of individual recombinants of E30 provides the means to document in detail the dynamics of E30 population turnover, geographical ranges of enterovirus transmission networks, and, ultimately, the relationship between the emergence of new variants of E30 and longer-term changes in disease associations and pathogenicity.     

Optimal Transmission Radius for Flooding in Large Scale Sensor Networks

One of the principal characteristics of large scale wireless sensor networks is their distributed, multi-hop nature. Due to this characteristic, applications such as query propagation rely regularly on network-wide flooding for information dissemination. If the transmission radius is not set optimally, the flooded packet may be holding the transmission medium for longer periods than are necessary, reducing overall network throughput. We analyze the impact of the transmission radius on the average settling time—the time at which all nodes in the network finish transmitting the flooded packet. Our analytical model takes into account the behavior of the underlying contention-based MAC protocol, as well as edge effects and the size of the network. We show that for large wireless networks there exists an intermediate transmission radius which minimizes the settling time, corresponding to an optimal tradeoff between reception and contention times. We also explain how physical propagation models affect small wireless networks and why there is no intermediate optimal transmission radius observed in these cases. The mathematical analysis is supported and validated through extensive simulations.Marco Zuniga is currently a PhD student in the Department of Electrical Engineering at the University of Southern California. He received his Bachelors degree in Electrical Engineering from the Pontificia Universidad Catolica del Peru in 1998, and his Masters degree in Electrical Engineering from the University of Southern California in 2002. His interests are in the area of Wireless Sensor Networks in general, and more specifically in studying the interaction amongst different layers to improve the performance of these networks. He is a member of IEEE and the Phi Kappa Phi Honor society.Bhaskar Krishnamachari is an Assistant Professor in the Department of Electrical Engineering at the University of Southern California (USC), where he also holds a joint appointment in the Department of Computer Science. He received his Bachelors degree in Electrical Engineering with a four-year full-tuition scholarship from The Cooper Union for the Advancement of Science and Art in 1998. He received his Masters degree and his Ph.D. in Electrical Engineering from Cornell University in 1999 and 2002, under a four-year university graduate fellowship. Dr. Krishnamacharis previous research has included work on critical density thresholds in wireless networks, data centric routing in sensor networks, mobility management in cellular telephone systems, multicast flow control, heuristic global optimization, and constraint satisfaction. His current research is focused on the discovery of fundamental principles and the analysis and design of protocols for next generation wireless sensor networks. He is a member of IEEE, ACM and the Tau Beta Pi and Eta Kappa Nu Engineering Honor Societies