Imperial College London

DrErikVolz

Faculty of MedicineSchool of Public Health

Lecturer in Population Biology of Infectious Diseases
 
 
 
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Contact

 

+44 (0)20 7594 1933e.volz Website

 
 
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Location

 

UG10Norfolk PlaceSt Mary's Campus

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Summary

 

Publications

Publication Type
Year
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45 results found

Ratmann O, Hodcroft EB, Pickles M, Cori A, Hall M, Lycett S, Colijn C, Dearlove B, Didelot X, Frost S, Hossain ASMM, Joy JB, Kendall M, Kuhnert D, Leventhal GE, Liang R, Plazzotta G, Poon AFY, Rasmussen DA, Stadler T, Volz E, Weis C, Brown AJL, Fraser C, Ratmann O, Hodcroft EB, Pickles M, Cori A, Hall M, Lycett S, Colijn C, Dearlove B, Didelot X, Frost S, Hossain AS, Joy JB, Kendall M, Kühnert D, Leventhal GE, Liang R, Plazzotta G, Poon AF, Rasmussen DA, Stadler T, Volz E, Weis C, Leigh Brown AJ, Fraser C, PANGEA-HIV Consortium, Ratmann O, Hodcroft EB, Pickles M, Cori A, Hall M, Lycett S, Colijn C, Dearlove B, Didelot X, Frost S, Md Mukarram Hossain AS, Joy JB, Kendall M, Kuhnert D, Leventhal GE, Liang R, Plazzotta G, Poon AFY, Rasmussen DA, Stadler T, Volz E, Weis C, Brown AJL, Fraser C, Ratmann O, Hodcroft EB, Pickles M, Cori A, Hall M, Lycett S, Colijn C, Dearlove B, Didelot X, Frost S, Hossain ASMM, Joy JB, Kendall M, Kühnert D, Leventhal GE, Liang R, Plazzotta G, Poon AFY, Rasmussen DA, Stadler T, Volz E, Weis C, Leigh Brown AJ, Fraser C, PANGEA-HIV Consortium, Ratmann O, Hodcroft EB, Pickles M, Cori A, Hall M, Lycett S, Colijn C, Dearlove B, Didelot X, Frost S, Hossain ASMM, Joy JB, Kendall M, Kühnert D, Leventhal GE, Liang R, Plazzotta G, Poon AFY, Rasmussen DA, Stadler T, Volz E, Weis C, Leigh Brown AJ, Fraser C, Ratmann O, Hodcroft EB, Pickles M, Cori A, Hall M, Lycett S, Colijn C, Dearlove B, Didelot X, Frost S, Hossain M, Joy JB, Kendall M, Kühnert D, Leventhal GE, Liang R, Plazzotta G, Poon A, Rasmussen DA, Stadler T, Volz E, Weis C, Leigh Brown AJ, Fraser Cet al., 2017, Phylogenetic Tools for Generalized HIV-1 Epidemics: Findings from the PANGEA-HIV Methods Comparison, MOLECULAR BIOLOGY AND EVOLUTION, Vol: 34, Pages: 185-203, ISSN: 0737-4038

Viral phylogenetic methods contribute to understanding how HIV spreads in populations, and thereby help guide the design of prevention interventions. So far, most analyses have been applied to well-sampled concentrated HIV-1 epidemics in wealthy countries. To direct the use of phylogenetic tools to where the impact of HIV-1 is greatest, the Phylogenetics And Networks for Generalized HIV Epidemics in Africa (PANGEA-HIV) consortium generates full-genome viral sequences from across sub-Saharan Africa. Analyzing these data presents new challenges, since epidemics are principally driven by heterosexual transmission and a smaller fraction of cases is sampled. Here, we show that viral phylogenetic tools can be adapted and used to estimate epidemiological quantities of central importance to HIV-1 prevention in sub-Saharan Africa. We used a community-wide methods comparison exercise on simulated data, where participants were blinded to the true dynamics they were inferring. Two distinct simulations captured generalized HIV-1 epidemics, before and after a large community-level intervention that reduced infection levels. Five research groups participated. Structured coalescent modeling approaches were most successful: phylogenetic estimates of HIV-1 incidence, incidence reductions, and the proportion of transmissions from individuals in their first 3 months of infection correlated with the true values (Pearson correlation > 90%), with small bias. However, on some simulations, true values were markedly outside reported confidence or credibility intervals. The blinded comparison revealed current limits and strengths in using HIV phylogenetics in challenging settings, provided benchmarks for future methods' development, and supports using the latest generation of phylogenetic tools to advance HIV surveillance and prevention.

JOURNAL ARTICLE

Sadasivam RS, Cutrona SL, Luger TM, Volz E, Kinney R, Rao SR, Allison JJ, Houston TK, Sadasivam RS, Cutrona SL, Luger TM, Volz E, Kinney R, Rao SR, Allison JJ, Houston TK, Sadasivam RS, Cutrona SL, Luger TM, Volz E, Kinney R, Rao SR, Allison JJ, Houston TK, Sadasivam RS, Cutrona SL, Luger TM, Volz E, Kinney R, Rao SR, Allison JJ, Houston TK, Sadasivam RS, Cutrona SL, Luger TM, Volz E, Kinney R, Rao SR, Allison JJ, Houston TK, Sadasivam RS, Cutrona SL, Luger TM, Volz E, Kinney R, Rao SR, Allison JJ, Houston TKet al., 2017, Share2Quit: Online Social Network Peer Marketing of Tobacco Cessation Systems, NICOTINE & TOBACCO RESEARCH, Vol: 19, Pages: 314-323, ISSN: 1462-2203

Introduction: Although technology-assisted tobacco interventions (TATIs) are effective, they are underused due to recruitment challenges. We tested whether we could successfully recruit smokers to a TATI using peer marketing through a social network (Facebook). Methods: We recruited smokers on Facebook using online advertisements. These recruited smokers (seeds) and subsequent waves of smokers (peer recruits) were provided the Share2Quit peer recruitment Facebook app and other tools. Smokers were incentivized for up to seven successful peer recruitments and had 30 days to recruit from date of registration. Successful peer recruitment was defined as a peer recruited smoker completing the registration on the TATI following a referral. Our primary questions were (1) whether smokers would recruit other smokers and (2) whether peer recruitment would extend the reach of the intervention to harder-to-reach groups, including those not ready to quit and minority smokers. Results: Overall, 759 smokers were recruited (seeds: 190; peer recruits: 569). Fifteen percent (n = 117) of smokers successfully recruited their peers (seeds: 24.7%; peer recruits: 7.7%) leading to four recruitment waves. Compared to seeds, peer recruits were less likely to be ready to quit (peer recruits 74.2% vs. seeds 95.1%), more likely to be male (67.1% vs. 32.9%), and more likely to be African American (23.8% vs. 10.8%) (p < .01 for all comparisons). Conclusions: Peer marketing quadrupled our engaged smokers and enriched the sample with not-ready-to-quit and African American smokers. Peer recruitment is promising, and our study uncovered several important challenges for future research. Implications: This study demonstrates the successful recruitment of smokers to a TATI using a Facebook-based peer marketing strategy. Smokers on Facebook were willing and able to recruit other smokers to a TATI, yielding a large and diverse population of smokers.

JOURNAL ARTICLE

Siveroni IA, Volz EM, 2017, PhyDyn: Epidemiological Modelling in BEAST

PhyDyn is a BEAST2 package for performing Bayesian phylogenetic inference under models that deal with structured populations with complex population dynamics. This package enables simultaneous estimation of epidemiological parameters and pathogen phylogenies.PhyDyn implements a structured coalescent model for a large class of epidemic processes specified by a deterministic nonlinear dynamical system, and computes the log-likelihood of a gene genealogy conditional on a complex demographic history. Genealogies are specified as timed phylogenetic trees in which lineages are associated with the distinct subpopulation in which they are sampled. Epidemic models are defined by a series of ordinary differential equations (ODEs) specifying the rates that new lineages introduced in the population (birth matrix) and the rates at which migrations, or transition between states occur (migration matrix).

SOFTWARE

Volz EM, Ndembi N, Nowak R, Kijak GH, Idoko J, Dakum P, Royal W, Baral S, Dybul M, Blattner WA, Charurat M, Volz EM, Ndembi N, Nowak R, Kijak GH, Idoko J, Dakum P, Royal W, Baral S, Dybul M, Blattner WA, Charurat Met al., 2017, Phylodynamic analysis to inform prevention efforts in mixed HIV epidemics., Virus Evol, Vol: 3, ISSN: 2057-1577

In HIV epidemics of Sub Saharan Africa, the utility of HIV prevention efforts focused on key populations at higher risk of HIV infection and transmission is unclear. We conducted a phylodynamic analysis of HIV-1 pol sequences from four different risk groups in Abuja, Nigeria to estimate transmission patterns between men who have sex with men (MSM) and a representative sample of newly enrolled treatment naive HIV clients without clearly recorded HIV acquisition risks. We develop a realistic dynamical infectious disease model which was fitted to time-scaled phylogenies for subtypes G and CRF02_AG using a structured-coalescent approach. We compare the infectious disease model and structured coalescent to commonly used genetic clustering methods. We estimate HIV incidence among MSM of 7.9% (95%CI, 7.0-10.4) per susceptible person-year, and the population attributable fraction of HIV transmissions from MSM to reproductive age females to be 9.1% (95%CI, 3.8-18.6), and from the reproductive age women to MSM as 0.2% (95%CI, 0.06-0.3). Applying these parameter estimates to evaluate a test-and-treat HIV strategy that target MSM reduces the total HIV infections averted by half with a 2.5-fold saving. These results suggest the importance of addressing the HIV treatment needs of MSM in addition to cost-effectiveness of specific scale-up of treatment for MSM in the context of the mixed HIV epidemic observed in Nigeria.

JOURNAL ARTICLE

Volz EM, Romero-Severson E, Leitner T, Volz EM, Romero-Severson E, Leitner T, Volz EM, Romero-Severson E, Leitner T, Volz EM, Romero-Severson E, Leitner T, Volz EM, Romero-Severson E, Leitner T, Volz E, Romero-Severson E, Leitner TKet al., 2017, Phylodynamic Inference across Epidemic Scales, MOLECULAR BIOLOGY AND EVOLUTION, Vol: 34, Pages: 1276-1288, ISSN: 0737-4038

Within-host genetic diversity and large transmission bottlenecks confound phylodynamic inference of epidemiological dynamics. Conventional phylodynamic approaches assume that nodes in a time-scaled pathogen phylogeny correspond closely to the time of transmission between hosts that are ancestral to the sample. However, when hosts harbor diverse pathogen populations, node times can substantially pre-date infection times. Imperfect bottlenecks can cause lineages sampled in different individuals to coalesce in unexpected patterns. To address realistic violations of standard phylodynamic assumptions we developed a new inference approach based on a multi-scale coalescent model, accounting for nonlinear epidemiological dynamics, heterogeneous sampling through time, non-negligible genetic diversity of pathogens within hosts, and imperfect transmission bottlenecks. We apply this method to HIV-1 and Ebola virus (EBOV) outbreak sequence data, illustrating how and when conventional phylodynamic inference may give misleading results. Within-host diversity of HIV-1 causes substantial upwards bias in the number of infected hosts using conventional coalescent models, but estimates using the multi-scale model have greater consistency with reported number of diagnoses through time. In contrast, we find that within-host diversity of EBOV has little influence on estimated numbers of infected hosts or reproduction numbers, and estimates are highly consistent with the reported number of diagnoses through time. The multi-scale coalescent also enables estimation of within-host effective population size using single sequences from a random sample of patients. We find within-host population genetic diversity of HIV-1 p17 to be 2Nμ=0.012 (95% CI 0.0066-0.023), which is lower than estimates based on HIV envelope serial sequencing of individual patients.

JOURNAL ARTICLE

Aiello AE, Simanek AM, Eisenberg MC, Walsh AR, Davis B, Volz E, Cheng C, Rainey JJ, Uzicanin A, Gao H, Osgood N, Knowles D, Stanley K, Tarter K, Monto AS, Aiello AE, Simanek AM, Eisenberg MC, Walsh AR, Davis B, Volz E, Cheng C, Rainey JJ, Uzicanin A, Gao H, Osgood N, Knowles D, Stanley K, Tarter K, Monto AS, Aiello AE, Simanek AM, Eisenberg MC, Walsh AR, Davis B, Volz E, Cheng C, Rainey JJ, Uzicanin A, Gao H, Osgood N, Knowles D, Stanley K, Tarter K, Monto AS, Aiello AE, Simanek AM, Eisenberg MC, Walsh AR, Davis B, Volz E, Cheng C, Rainey JJ, Uzicanin A, Gao H, Osgood N, Knowles D, Stanley K, Tarter K, Monto AS, Aiello AE, Simanek AM, Eisenberg MC, Walsh AR, Davis B, Volz E, Cheng C, Rainey JJ, Uzicanin A, Gao H, Osgood N, Knowles D, Stanley K, Tarter K, Monto AS, Aiello AE, Simanek AM, Eisenberg MC, Walsh AR, Davis B, Volz E, Cheng C, Rainey JJ, Uzicanin A, Gao H, Osgood N, Knowles D, Stanley K, Tarter K, Monto ASet al., 2016, Design and methods of a social network isolation study for reducing respiratory infection transmission: The eX-FLU cluster randomized trial, EPIDEMICS, Vol: 15, Pages: 38-55, ISSN: 1755-4365

BACKGROUND: Social networks are increasingly recognized as important points of intervention, yet relatively few intervention studies of respiratory infection transmission have utilized a network design. Here we describe the design, methods, and social network structure of a randomized intervention for isolating respiratory infection cases in a university setting over a 10-week period. METHODOLOGY/PRINCIPAL FINDINGS: 590 students in six residence halls enrolled in the eX-FLU study during a chain-referral recruitment process from September 2012-January 2013. Of these, 262 joined as "seed" participants, who nominated their social contacts to join the study, of which 328 "nominees" enrolled. Participants were cluster-randomized by 117 residence halls. Participants were asked to respond to weekly surveys on health behaviors, social interactions, and influenza-like illness (ILI) symptoms. Participants were randomized to either a 3-Day dorm room isolation intervention or a control group (no isolation) upon illness onset. ILI cases reported on their isolation behavior during illness and provided throat and nasal swab specimens at onset, day-three, and day-six of illness. A subsample of individuals (N=103) participated in a sub-study using a novel smartphone application, iEpi, which collected sensor and contextually-dependent survey data on social interactions. Within the social network, participants were significantly positively assortative by intervention group, enrollment type, residence hall, iEpi participation, age, gender, race, and alcohol use (all P<0.002). CONCLUSIONS/SIGNIFICANCE: We identified a feasible study design for testing the impact of isolation from social networks in a university setting. These data provide an unparalleled opportunity to address questions about isolation and infection transmission, as well as insights into social networks and behaviors among college-aged students. Several important lessons were learned over the cour

JOURNAL ARTICLE

Volz E, Nowak R, Ndembi N, Kijak G, Baral S, Blattner W, Charurat Met al., 2016, Genetic Diversity of HIV Reveals the Epidemiological Role of High Risk Groups in Nigeria, 17th Annual International Meeting of the Institute-of-Human-Virology at the University-of-Maryland-School-of-Medicine, Publisher: LIPPINCOTT WILLIAMS & WILKINS, Pages: 47-47, ISSN: 1525-4135

CONFERENCE PAPER

Romero-Severson EO, Volz E, Koopman JS, Leitner T, Ionides EL, Romero-Severson EO, Volz E, Koopman JS, Leitner T, Ionides ELet al., 2015, Dynamic Variation in Sexual Contact Rates in a Cohort of HIV-Negative Gay Men, American Journal of Epidemiology, Vol: 182, Pages: 255-262, ISSN: 0002-9262

Human immunodeficiency virus (HIV) transmission models that include variability in sexual behavior over timehave shown increased incidence, prevalence, and acute-state transmission rates for a given population risk profile.This raises the question of whether dynamic variation in individual sexual behavior is a real phenomenon that can beobserved and measured. To study this dynamic variation, we developed a model incorporating heterogeneity inboth between-person and within-person sexual contact patterns. Using novel methodology that we call iterated filteringfor longitudinal data, we fitted this model by maximum likelihood to longitudinal survey data from the Centersfor Disease Control and Prevention’s Collaborative HIV Seroincidence Study (1992–1995). We found evidence forindividual heterogeneity in sexual behavior over time. We simulated an epidemic process and found that inclusion ofempirically measured levels of dynamic variation in individual-level sexual behavior brought the theoretical predictionsof HIV incidence into closer alignment with reality given the measured per-act probabilities of transmission.The methods developed here provide a framework for quantifying variation in sexual behaviors that helps in understandingthe HIV epidemic among gay men.

JOURNAL ARTICLE

Rasmussen DA, Volz EM, Koelle K, Rasmussen DA, Volz EM, Koelle K, Rasmussen DA, Volz EM, Koelle K, Rasmussen DA, Volz EM, Koelle K, Rasmussen DA, Volz EM, Koelle Ket al., 2014, Phylodynamic Inference for Structured Epidemiological Models, PLOS COMPUTATIONAL BIOLOGY, Vol: 10, Pages: e1003570-e1003570, ISSN: 1553-734X

Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.

JOURNAL ARTICLE

Romero-Severson EO, Meadors GD, Volz EM, Romero-Severson EO, Meadors GD, Volz EM, Romero-Severson EO, Meadors GD, Volz EM, Romero-Severson EO, Meadors GD, Volz EMet al., 2014, A generating function approach to HIV transmission with dynamic contact rates., Math Model Nat Phenom, Vol: 9, Pages: 121-135, ISSN: 0973-5348

The basic reproduction number, R0, is often defined as the average number of infections generated by a newly infected individual in a fully susceptible population. The interpretation, meaning, and derivation of R0 are controversial. However, in the context of mean field models, R0 demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this manner, R0 has been proposed as a method for understanding the relative impact of public health interventions with respect to disease eliminations from a theoretical perspective. The use of R0 is made more complex by both the strong dependency of R0 on the model form and the stochastic nature of transmission. A common assumption in models of HIV transmission that have closed form expressions for R0 is that a single individual's behavior is constant over time. In this paper we derive expressions for both R0 and probability of an epidemic in a finite population under the assumption that people periodically change their sexual behavior over time. We illustrate the use of generating functions as a general framework to model the effects of potentially complex assumptions on the number of transmissions generated by a newly infected person in a susceptible population. We find that the relationship between the probability of an epidemic and R0 is not straightforward, but, that as the rate of change in sexual behavior increases both R0 and the probability of an epidemic also decrease.

JOURNAL ARTICLE

Volz E, Pond S, Volz E, Pond S, Volz E, Pond S, Volz E, Pond Set al., 2014, Phylodynamic analysis of ebola virus in the 2014 sierra leone epidemic., PLoS Curr, Vol: 6, ISSN: 2157-3999

BACKGROUND: The Ebola virus (EBOV) epidemic in Western Africa is the largest in recorded history and control efforts have so far failed to stem the rapid growth in the number of infections. Mathematical models serve a key role in estimating epidemic growth rates and the reproduction number (R0) from surveillance data and, recently, molecular sequence data. Phylodynamic analysis of existing EBOV time-stamped sequence data may provide independent estimates of the unobserved number of infections, reveal recent epidemiological history, and provide insight into selective pressures acting upon viral genes. METHODS: We fit a series mathematical models of infectious disease dynamics to phylogenies estimated from 78 whole EBOV genomes collected from distinct patients in May and June of 2014 in Sierra Leone, and perform evolutionary analysis on these genomes combined with closely related EBOV genomes from previous outbreaks. Two analyses are conducted with values of the latent period that have been used in recent modelling efforts. We also examined the EBOV sequences for evidence of possible episodic adaptive molecular evolution during the 2014 outbreak. RESULTS: We find evidence for adaptive evolution affecting L and GP protein coding regions of the EBOV genome, which is unlikely to bias molecular clock and phylodynamic analyses. We estimate R0=2.40 (95% HPD:1.54-3.87 ) if the mean latent period is 5.3 days, and R0=3.81, (95% HPD:2.47-6.3) if the mean latent period is 12.7 days. The estimated coefficient of variation (CV) of the number of transmissions per infected host is very high, and a large proportion of infections yield no transmissions. CONCLUSIONS: Estimates of R0 are sensitive to the unknown latent infectious period which can not be reliably estimated from genetic data alone. EBOV phylogenies show significant evidence for superspreading and extreme variance in the number of transmissions per infected individual during the early epidemic in Sierra Leone.

JOURNAL ARTICLE

Volz EM, Frost SDW, Volz EM, Frost SDW, Volz EM, Frost SDW, Volz EM, Frost SD, Volz EM, Frost SDW, Volz EM, Frost SDWet al., 2014, Sampling through time and phylodynamic inference with coalescent and birth-death models, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 11, Pages: 20140945-20140945, ISSN: 1742-5689

Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the birth–death-sampling model (BDM), in the context of estimating population size and birth rates in a population growing exponentially according to the birth–death branching process. For sequences sampled at a single time, we found the coalescent and the BDM gave virtually indistinguishable results in terms of the growth rates and fraction of the population sampled, even when sampling from a small population. For sequences sampled at multiple time points, we find that the birth–death model estimators are subject to large bias if the sampling process is misspecified. Since BDMs incorporate a model of the sampling process, we show how much of the statistical power of BDMs arises from the sequence of sample times and not from the genealogical tree. This motivates the development of a new coalescent estimator, which is augmented with a model of the known sampling process and is potentially more precise than the coalescent that does not use sample time information.

JOURNAL ARTICLE

Alam SJ, Zhang X, Romero-Severson EO, Henry C, Zhong L, Volz EM, Brenner BG, Koopman JS, Alam SJ, Zhang X, Romero-Severson EO, Henry C, Zhong L, Volz EM, Brenner BG, Koopman JS, Alam SJ, Zhang X, Romero-Severson EO, Henry C, Zhong L, Volz EM, Brenner BG, Koopman JS, Alam SJ, Zhang X, Romero-Severson EO, Henry C, Zhong L, Volz EM, Brenner BG, Koopman JSet al., 2013, Detectable signals of episodic risk effects on acute HIV transmission: strategies for analyzing transmission systems using genetic data., Epidemics, Vol: 5, Pages: 44-55, ISSN: 1755-4365

Episodic high-risk sexual behavior is common and can have a profound effect on HIV transmission. In a model of HIV transmission among men who have sex with men (MSM), changing the frequency, duration and contact rates of high-risk episodes can take endemic prevalence from zero to 50% and more than double transmissions during acute HIV infection (AHI). Undirected test and treat could be inefficient in the presence of strong episodic risk effects. Partner services approaches that use a variety of control options will be likely to have better effects under these conditions, but the question remains: What data will reveal if a population is experiencing episodic risk effects? HIV sequence data from Montreal reveals genetic clusters whose size distribution stabilizes over time and reflects the size distribution of acute infection outbreaks (AIOs). Surveillance provides complementary behavioral data. In order to use both types of data efficiently, it is essential to examine aspects of models that affect both the episodic risk effects and the shape of transmission trees. As a demonstration, we use a deterministic compartmental model of episodic risk to explore the determinants of the fraction of transmissions during acute HIV infection (AHI) at the endemic equilibrium. We use a corresponding individual-based model to observe AIO size distributions and patterns of transmission within AIO. Episodic risk parameters determining whether AHI transmission trees had longer chains, more clustered transmissions from single individuals, or different mixes of these were explored. Encouragingly for parameter estimation, AIO size distributions reflected the frequency of transmissions from acute infection across divergent parameter sets. Our results show that episodic risk dynamics influence both the size and duration of acute infection outbreaks, thus providing a possible link between genetic cluster size distributions and episodic risk dynamics.

JOURNAL ARTICLE

Frost SDW, Volz EM, Frost SDW, Volz EMet al., 2013, Modelling tree shape and structure in viral phylodynamics, Philosophical Transactions of the Royal Society B: Biological Sciences, Vol: 368, Pages: 20120208-20120208, ISSN: 0962-8436

Epidemiological models have highlighted the importance of population structure in the transmission dynamics of infectious diseases. Using HIV-1 as an example of a model evolutionary system, we consider how population structure affects the shape and the structure of a viral phylogeny in the absence of strong selection at the population level. For structured populations, the number of lineages as a function of time is insufficient to describe the shape of the phylogeny. We develop deterministic approximations for the dynamics of tips of the phylogeny over evolutionary time, the number of 'cherries', tips that share a direct common ancestor, and Sackin's index, a commonly used measure of phylogenetic imbalance or asymmetry. We employ cherries both as a measure of asymmetry of the tree aswell as ameasure of the association between sequences from different groups. We consider heterogeneity in infectiousness associated with different stages of HIV infection, and in contact rates between groups of individuals. In the absence of selection, we find that population structure may have relatively little impact on the overall asymmetry of a tree, especially when only a small fraction of infected individuals is sampled, but may have marked effects on how sequences from different subpopulations cluster and co-cluster. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

JOURNAL ARTICLE

Frost SDW, Volz EM, Frost SDW, Volz EM, Frost SD, Volz EMet al., 2013, Modelling tree shape and structure in viral phylodynamics., Philos Trans R Soc Lond B Biol Sci, Vol: 368, ISSN: 0962-8436

Epidemiological models have highlighted the importance of population structure in the transmission dynamics of infectious diseases. Using HIV-1 as an example of a model evolutionary system, we consider how population structure affects the shape and the structure of a viral phylogeny in the absence of strong selection at the population level. For structured populations, the number of lineages as a function of time is insufficient to describe the shape of the phylogeny. We develop deterministic approximations for the dynamics of tips of the phylogeny over evolutionary time, the number of 'cherries', tips that share a direct common ancestor, and Sackin's index, a commonly used measure of phylogenetic imbalance or asymmetry. We employ cherries both as a measure of asymmetry of the tree as well as a measure of the association between sequences from different groups. We consider heterogeneity in infectiousness associated with different stages of HIV infection, and in contact rates between groups of individuals. In the absence of selection, we find that population structure may have relatively little impact on the overall asymmetry of a tree, especially when only a small fraction of infected individuals is sampled, but may have marked effects on how sequences from different subpopulations cluster and co-cluster.

JOURNAL ARTICLE

Miller JC, Volz EM, 2013, Incorporating Disease and Population Structure into Models of SIR Disease in Contact Networks, PloS one, Vol: 8, Pages: e69162-e69162

JOURNAL ARTICLE

Miller JC, Volz EM, Miller JC, Volz EM, Miller JC, Volz EM, Miller JC, Volz EMet al., 2013, Model hierarchies in edge-based compartmental modeling for infectious disease spread., J Math Biol, Vol: 67, Pages: 869-899, ISSN: 0303-6812

We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the mass action model gives clear, rigorous conditions under which the mass action model is accurate.

JOURNAL ARTICLE

Romero-Severson EO, Alam SJ, Volz E, Koopman J, Romero-Severson EO, Alam SJ, Volz E, Koopman J, Romero-Severson EO, Alam SJ, Volz E, Koopman J, Romero-Severson EO, Alam SJ, Volz E, Koopman Jet al., 2013, Acute-stage transmission of HIV: effect of volatile contact rates., Epidemiology, Vol: 24, Pages: 516-521, ISSN: 1044-3983

BACKGROUND: The role of acute-stage transmission in sustaining HIV epidemics has been difficult to determine. This difficulty is exacerbated by a lack of theoretical understanding of how partnership dynamics and sexual behavior interact to affect acute-stage transmission. We propose that individual-level variation in rates of sexual contact is a key aspect of partnership dynamics that can greatly increase acute-stage HIV transmission. METHODS: Using an individual-based stochastic framework, we simulated a model of HIV transmission that includes individual-level changes in contact rates. We report both population-level statistics (such as prevalence and acute-stage transmission rates) and individual-level statistics (such as the contact rate at the time of infection). RESULTS: Volatility increases both the prevalence of HIV and the proportion of new cases from acute-stage infectors. These effects result from 1) a relative reduction in transmission rate from chronic but not acute infectors and 2) an increase in the availability of high-risk susceptibles. CONCLUSIONS: The extent of changes in individual-level contact rates in the real world is unknown. Aggregate or strictly cross-sectional data do not reveal individual-level changes in partnership dynamics and sexual behavior. The strong effects presented in this article motivate both continued theoretical exploration of volatility in sexual behavior and collection of longitudinal individual-level data to inform more realistic models.

JOURNAL ARTICLE

Sadasivam RS, Cutrona SL, Volz E, Rao SR, Houston TK, Sadasivam RS, Cutrona SL, Volz E, Rao SR, Houston TK, Sadasivam RS, Cutrona SL, Volz E, Rao SR, Houston TKet al., 2013, Web-based peer-driven chain referrals for smoking cessation., Stud Health Technol Inform, Vol: 192, Pages: 357-361, ISSN: 0926-9630

BACKGROUND: We are testing web-based respondent-driven sampling (RDS) chain referrals to recruit smokers to the Decide2Quit.org (D2Q) web-assisted tobacco intervention. METHODS: Using an online survey of smokers, we assessed the potential of recruiting 1200 smokers in 9 months using RDS chain referrals. RDS is a complex sample design, and many factors can influence its success. We conducted simulations to determine the design of optimal RDS chains. RESULTS: Smokers (n=48) were mostly female (72%) and between ages 30-60 (82%). Estimation of smokers in their network: 1-5 (40%), 6-10 (24%), and 10-20 (22%), with mean number of intimate family (2.2, SD=2.1) and close friend smokers (3.7, SD=3.8). Most smokers (82%) were willing to refer to D2Q and thought their friends (mean=5.0, SD=4.4, range=0-20) would be open to referral. Simulations suggested that with a quota of 3 and 10 seeds, 99.9% of the sample would be achieved in 107 days if the acceptance probability was 0.5. Acceptance probability of 25% would necessitate an increased quota. CONCLUSIONS: Our study suggests that it is possible to recruit smokers using RDS.

JOURNAL ARTICLE

Sadasivam RS, Volz EM, Kinney RL, Rao SR, Houston TK, Sadasivam RS, Volz EM, Kinney RL, Rao SR, Houston TK, Sadasivam RS, Volz EM, Kinney RL, Rao SR, Houston TK, Sadasivam RS, Volz EM, Kinney RL, Rao SR, Houston TKet al., 2013, Share2Quit: Web-Based Peer-Driven Referrals for Smoking Cessation., JMIR Res Protoc, Vol: 2, Pages: e37-e37, ISSN: 1929-0748

BACKGROUND: Smoking is the number one preventable cause of death in the United States. Effective Web-assisted tobacco interventions are often underutilized and require new and innovative engagement approaches. Web-based peer-driven chain referrals successfully used outside health care have the potential for increasing the reach of Internet interventions. OBJECTIVE: The objective of our study was to describe the protocol for the development and testing of proactive Web-based chain-referral tools for increasing the access to Decide2Quit.org, a Web-assisted tobacco intervention system. METHODS: We will build and refine proactive chain-referral tools, including email and Facebook referrals. In addition, we will implement respondent-driven sampling (RDS), a controlled chain-referral sampling technique designed to remove inherent biases in chain referrals and obtain a representative sample. We will begin our chain referrals with an initial recruitment of former and current smokers as seeds (initial participants) who will be trained to refer current smokers from their social network using the developed tools. In turn, these newly referred smokers will also be provided the tools to refer other smokers from their social networks. We will model predictors of referral success using sample weights from the RDS to estimate the success of the system in the targeted population. RESULTS: This protocol describes the evaluation of proactive Web-based chain-referral tools, which can be used in tobacco interventions to increase the access to hard-to-reach populations, for promoting smoking cessation. CONCLUSIONS: Share2Quit represents an innovative advancement by capitalizing on naturally occurring technology trends to recruit smokers to Web-assisted tobacco interventions.

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Volz EM, Frost SDW, Volz EM, Frost SDW, Volz EM, Frost SDW, Volz EM, Frost SD, Volz EM, Frost SDWet al., 2013, Inferring the Source of Transmission with Phylogenetic Data, PLOS COMPUTATIONAL BIOLOGY, Vol: 9, Pages: e1003397-e1003397, ISSN: 1553-7358

Identifying the source of transmission using pathogen genetic data is complicated by numerous biological, immunological, and behavioral factors. A large source of error arises when there is incomplete or sparse sampling of cases. Unsampled cases may act as either a common source of infection or as an intermediary in a transmission chain for hosts infected with genetically similar pathogens. It is difficult to quantify the probability of common source or intermediate transmission events, which has made it difficult to develop statistical tests to either confirm or deny putative transmission pairs with genetic data. We present a method to incorporate additional information about an infectious disease epidemic, such as incidence and prevalence of infection over time, to inform estimates of the probability that one sampled host is the direct source of infection of another host in a pathogen gene genealogy. These methods enable forensic applications, such as source-case attribution, for infectious disease epidemics with incomplete sampling, which is usually the case for high-morbidity community-acquired pathogens like HIV, Influenza and Dengue virus. These methods also enable epidemiological applications such as the identification of factors that increase the risk of transmission. We demonstrate these methods in the context of the HIV epidemic in Detroit, Michigan, and we evaluate the suitability of current sequence databases for forensic and epidemiological investigations. We find that currently available sequences collected for drug resistance testing of HIV are unlikely to be useful in most forensic investigations, but are useful for identifying transmission risk factors.

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Volz EM, Ionides E, Romero-Severson EO, Brandt M-G, Mokotoff E, Koopman JS, Volz EM, Ionides E, Romero-Severson EO, Brandt M-G, Mokotoff E, Koopman JS, Volz EM, Ionides E, Romero-Severson EO, Brandt MG, Mokotoff E, Koopman JS, Volz EM, Ionides E, Romero-Severson EO, Brandt M-G, Mokotoff E, Koopman JS, Volz EM, Ionides E, Romero-Severson EO, Brandt M-G, Mokotoff E, Koopman JSet al., 2013, HIV-1 Transmission during Early Infection in Men Who Have Sex with Men: A Phylodynamic Analysis, PLOS MEDICINE, Vol: 10, Pages: e1001568-12, ISSN: 1549-1676

BACKGROUND: Conventional epidemiological surveillance of infectious diseases is focused on characterization of incident infections and estimation of the number of prevalent infections. Advances in methods for the analysis of the population-level genetic variation of viruses can potentially provide information about donors, not just recipients, of infection. Genetic sequences from many viruses are increasingly abundant, especially HIV, which is routinely sequenced for surveillance of drug resistance mutations. We conducted a phylodynamic analysis of HIV genetic sequence data and surveillance data from a US population of men who have sex with men (MSM) and estimated incidence and transmission rates by stage of infection. METHODS AND FINDINGS: We analyzed 662 HIV-1 subtype B sequences collected between October 14, 2004, and February 24, 2012, from MSM in the Detroit metropolitan area, Michigan. These sequences were cross-referenced with a database of 30,200 patients diagnosed with HIV infection in the state of Michigan, which includes clinical information that is informative about the recency of infection at the time of diagnosis. These data were analyzed using recently developed population genetic methods that have enabled the estimation of transmission rates from the population-level genetic diversity of the virus. We found that genetic data are highly informative about HIV donors in ways that standard surveillance data are not. Genetic data are especially informative about the stage of infection of donors at the point of transmission. We estimate that 44.7% (95% CI, 42.2%-46.4%) of transmissions occur during the first year of infection. CONCLUSIONS: In this study, almost half of transmissions occurred within the first year of HIV infection in MSM. Our conclusions may be sensitive to un-modeled intra-host evolutionary dynamics, un-modeled sexual risk behavior, and uncertainty in the stage of infected hosts at the time of sampling. The intensity of transmission during

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Volz EM, Koelle K, Bedford T, Volz EM, Koelle K, Bedford T, Volz EM, Koelle K, Bedford T, Volz EM, Koelle K, Bedford Tet al., 2013, Viral phylodynamics., PLoS Comput Biol, Vol: 9, Pages: e1002947-e1002947, ISSN: 1553-734X

Viral phylodynamics is defined as the study of how epidemiological, immunological, and evolutionary processes act and potentially interact to shape viralphylogenies. Since the coining of the term in 2004, research on viral phylodynamics has focused on transmission dynamics in an effort to shed light on how these dynamics impact viral genetic variation. Transmission dynamics can be considered at the level of cells within an infected host, individual hosts within a population, or entire populations of hosts. Many viruses, especially RNA viruses, rapidly accumulate genetic variation because of short generation times and high mutation rates. Patterns of viral genetic variation are therefore heavily influenced by how quickly transmission occurs and by which entities transmit to one another. Patterns of viral genetic variation will also be affected by selection acting on viral phenotypes. Although viruses can differ with respect to many phenotypes, phylodynamic studies have to date tended to focus on a limited number of viral phenotypes. These include virulence phenotypes, phenotypes associated with viral transmissibility, cell or tissue tropism phenotypes, and antigenic phenotypes that can facilitate escape from host immunity. Due to the impact that transmission dynamics and selection can have on viral genetic variation, viral phylogenies can therefore be used to investigate important epidemiological, immunological, and evolutionary processes, such as epidemic spread[2], spatio-temporal dynamics including metapopulation dynamics[3], zoonotic transmission, tissue tropism[4], and antigenic drift[5]. The quantitative investigation of these processes through the consideration of viral phylogenies is the central aim of viral phylodynamics.

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Bauermeister JA, Zimmerman MA, Johns MM, Glowacki P, Stoddard S, Volz E, Bauermeister JA, Zimmerman MA, Johns MM, Glowacki P, Stoddard S, Volz E, Bauermeister JA, Zimmerman MA, Johns MM, Glowacki P, Stoddard S, Volz E, Bauermeister JA, Zimmerman MA, Johns MM, Glowacki P, Stoddard S, Volz Eet al., 2012, Innovative recruitment using online networks: lessons learned from an online study of alcohol and other drug use utilizing a web-based, respondent-driven sampling (webRDS) strategy., J Stud Alcohol Drugs, Vol: 73, Pages: 834-838, ISSN: 1937-1888

OBJECTIVE: We used a web version of Respondent-Driven Sampling (webRDS) to recruit a sample of young adults (ages 18-24) and examined whether this strategy would result in alcohol and other drug (AOD) prevalence estimates comparable to national estimates (National Survey on Drug Use and Health [NSDUH]). METHOD: We recruited 22 initial participants (seeds) via Facebook to complete a web survey examining AOD risk correlates. Sequential, incentivized recruitment continued until our desired sample size was achieved. After correcting for webRDS clustering effects, we contrasted our AOD prevalence estimates (past 30 days) to NSDUH estimates by comparing the 95% confidence intervals of prevalence estimates. RESULTS: We found comparable AOD prevalence estimates between our sample and NSDUH for the past 30 days for alcohol, marijuana, cocaine, Ecstasy (3,4-methylenedioxymethamphetamine, or MDMA), and hallucinogens. Cigarette use was lower than NSDUH estimates. CONCLUSIONS: WebRDS may be a suitable strategy to recruit young adults online. We discuss the unique strengths and challenges that may be encountered by public health researchers using webRDS methods.

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Miller JC, Slim AC, Volz EM, Miller JC, Slim AC, Volz EM, Miller JC, Slim AC, Volz EM, Miller JC, Slim AC, Volz EMet al., 2012, Edge-based compartmental modelling for infectious disease spread., J R Soc Interface, Vol: 9, Pages: 890-906, ISSN: 1742-5689

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action susceptible-infected-recovered model of Kermack & McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes that all individuals have the same contact rate and partnerships are fleeting. In this study, we introduce edge-based compartmental modelling, a technique eliminating these assumptions. We derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of partnership duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model and focus on applying the technique under different assumptions about how contact rates are distributed and how long partnerships last.

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Romero-Severson EO, Alam SJ, Volz EM, Koopman JS, Romero-Severson EO, Alam SJ, Volz EM, Koopman JS, Romero-Severson EO, Alam SJ, Volz EM, Koopman JSet al., 2012, Heterogeneity in Number and Type of Sexual Contacts in a Gay Urban Cohort., Stat Commun Infect Dis, Vol: 4, ISSN: 1948-4690

HIV transmission models include heterogeneous individuals with different sexual behaviors including contact rates, mixing patterns, and sexual practices. However, heterogeneity can also exist within individuals over time. In this paper we analyze a two year prospective cohort of 882 gay men with observations at six month intervals focusing on heterogeneity both within and between individuals in sexual contact rates and sexual roles. The total number of sexual contacts made over the course of the study (mean 1.55 per month) are highly variable between individuals (standard deviation 9.82 per month) as expected. At the individual level, contacts were also heterogeneous over time. For a homogeneous count process the variance should scale with the mean; however, at the individual level the variance scaled with the square root of the mean implying the presence of heterogeneity within individuals over time. We also observed a high level of movement between dichotomous sexual roles (insertive/receptive, protected/unprotected, anal/oral, and HIV status of partners). On average periods of exclusively unprotected sexual contacted lasted 16 months. Our results suggest that future HIV models should consider heterogeneities both between and within individuals in sexual contact rates and sexual roles.

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Volz EM, Koopman JS, Ward MJ, Brown AL, Frost SD, Volz EM, Koopman JS, Ward MJ, Brown AL, Frost SDW, Volz EM, Koopman JS, Ward MJ, Brown AL, Frost SDW, Volz EM, Koopman JS, Ward MJ, Brown AL, Frost SDWet al., 2012, Simple epidemiological dynamics explain phylogenetic clustering of HIV from patients with recent infection., PLoS Comput Biol, Vol: 8, Pages: e1002552-e1002552, ISSN: 1553-734X

Phylogenies of highly genetically variable viruses such as HIV-1 are potentially informative of epidemiological dynamics. Several studies have demonstrated the presence of clusters of highly related HIV-1 sequences, particularly among recently HIV-infected individuals, which have been used to argue for a high transmission rate during acute infection. Using a large set of HIV-1 subtype B pol sequences collected from men who have sex with men, we demonstrate that virus from recent infections tend to be phylogenetically clustered at a greater rate than virus from patients with chronic infection ('excess clustering') and also tend to cluster with other recent HIV infections rather than chronic, established infections ('excess co-clustering'), consistent with previous reports. To determine the role that a higher infectivity during acute infection may play in excess clustering and co-clustering, we developed a simple model of HIV infection that incorporates an early period of intensified transmission, and explicitly considers the dynamics of phylogenetic clusters alongside the dynamics of acute and chronic infected cases. We explored the potential for clustering statistics to be used for inference of acute stage transmission rates and found that no single statistic explains very much variance in parameters controlling acute stage transmission rates. We demonstrate that high transmission rates during the acute stage is not the main cause of excess clustering of virus from patients with early/acute infection compared to chronic infection, which may simply reflect the shorter time since transmission in acute infection. Higher transmission during acute infection can result in excess co-clustering of sequences, while the extent of clustering observed is most sensitive to the fraction of infections sampled.

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Volz EM, Volz EM, Volz EM, Volz EMet al., 2012, Complex population dynamics and the coalescent under neutrality., Genetics, Vol: 190, Pages: 187-201, ISSN: 0016-6731

Estimates of the coalescent effective population size N(e) can be poorly correlated with the true population size. The relationship between N(e) and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of N(e) such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics.

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Zhang X, Zhong L, Romero-Severson E, Alam SJ, Henry CJ, Volz EM, Koopman JS, Zhang X, Zhong L, Romero-Severson E, Alam SJ, Henry CJ, Volz EM, Koopman JS, Zhang X, Zhong L, Romero-Severson E, Alam SJ, Henry CJ, Volz EM, Koopman JSet al., 2012, Episodic HIV Risk Behavior Can Greatly Amplify HIV Prevalence and the Fraction of Transmissions from Acute HIV Infection., Stat Commun Infect Dis, Vol: 4, ISSN: 1948-4690

A deterministic compartmental model was explored that relaxed the unrealistic assumption in most HIV transmission models that behaviors of individuals are constant over time. A simple model was formulated to better explain the effects observed. Individuals had a high and a low contact rate and went back and forth between them. This episodic risk behavior interacted with the short period of high transmissibility during acute HIV infection to cause dramatic increases in prevalence as the differences between high and low contact rates increased and as the duration of high risk better matched the duration of acute HIV infection. These same changes caused a considerable increase in the fraction of all transmissions that occurred during acute infection. These strong changes occurred despite a constant total number of contacts and a constant total transmission potential from acute infection. Two phenomena played a strong role in generating these effects. First, people were infected more often during their high contact rate phase and they remained with high contact rates during the highly contagious acute infection stage. Second, when individuals with previously low contact rates moved into an episodic high-risk period, they were more likely to be susceptible and thus provided more high contact rate susceptible individuals who could get infected. These phenomena make test and treat control strategies less effective and could cause some behavioral interventions to increase transmission. Signature effects on genetic patterns between HIV strains could make it possible to determine whether these episodic risk effects are acting in a population.

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Craft ME, Volz E, Packer C, Meyers LA, Craft ME, Volz E, Packer C, Meyers LA, Craft ME, Volz E, Packer C, Meyers LA, Craft ME, Volz E, Packer C, Meyers LAet al., 2011, Disease transmission in territorial populations: the small-world network of Serengeti lions., J R Soc Interface, Vol: 8, Pages: 776-786, ISSN: 1742-5689

Territoriality in animal populations creates spatial structure that is thought to naturally buffer disease invasion. Often, however, territorial populations also include highly mobile, non-residential individuals that potentially serve as disease superspreaders. Using long-term data from the Serengeti Lion Project, we characterize the contact network structure of a territorial wildlife population and address the epidemiological impact of nomadic individuals. As expected, pride contacts are dominated by interactions with neighbouring prides and interspersed by encounters with nomads as they wander throughout the ecosystem. Yet the pride-pride network also includes occasional long-range contacts between prides, making it surprisingly small world and vulnerable to epidemics, even without nomads. While nomads increase both the local and global connectivity of the network, their epidemiological impact is marginal, particularly for diseases with short infectious periods like canine distemper virus. Thus, territoriality in Serengeti lions may be less protective and non-residents less important for disease transmission than previously considered.

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