1
|
DeGruttola V, Nakazawa M, Lin T, Liu J, Goyal R, Little S, Tu X, Mehta S. Modeling homophily in dynamic networks with application to HIV molecular surveillance. BMC Infect Dis 2023; 23:656. [PMID: 37794364 PMCID: PMC10548762 DOI: 10.1186/s12879-023-08598-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2023] [Accepted: 09/11/2023] [Indexed: 10/06/2023] Open
Abstract
BACKGROUND Efforts to control the HIV epidemic can benefit from knowledge of the relationships between the characteristics of people who have transmitted HIV and those who became infected by them. Investigation of this relationship is facilitated by the use of HIV genetic linkage analyses, which allows inference about possible transmission events among people with HIV infection. Two persons with HIV (PWH) are considered linked if the genetic distance between their HIV sequences is less than a given threshold, which implies proximity in a transmission network. The tendency of pairs of nodes (in our case PWH) that share (or differ in) certain attributes to be linked is denoted homophily. Below, we describe a novel approach to modeling homophily with application to analyses of HIV viral genetic sequences from clinical series of participants followed in San Diego. Over the 22-year period of follow-up, increases in cluster size results from HIV transmissions to new people from those already in the cluster-either directly or through intermediaries. METHODS Our analytical approach makes use of a logistic model to describe homophily with regard to demographic, clinical, and behavioral characteristics-that is we investigate whether similarities (or differences) between PWH in these characteristics are associated with their sequences being linked. To investigate the performance of our methods, we conducted on a simulation study for which data sets were generated in a way that reproduced the structure of the observed database. RESULTS Our results demonstrated strong positive homophily associated with hispanic ethnicity, and strong negative homophily, with birth year difference. The second result implies that the larger the difference between the age of a newly-infected PWH and the average age for an available cluster, the lower the odds of a newly infected person joining that cluster. We did not observe homophily associated with prior diagnosis of sexually transmitted diseases. Our simulation studies demonstrated the validity of our approach for modeling homophily, by showing that the estimates it produced matched the specified values of the statistical network generating model. CONCLUSIONS Our novel methods provide a simple and flexible statistical network-based approach for modeling the growth of viral (or other microbial) genetic clusters from linkage to new infections based on genetic distance.
Collapse
Affiliation(s)
- Victor DeGruttola
- Division of Biostatistics and Bioinformatics Herbert Wertheim School of Public Health and Human Longevity Science, University of California, 9500 Gilman Dr., 92093-0628, San Diego, La Jolla, CA, USA.
| | | | - Tuo Lin
- Division of Biostatistics and Bioinformatics Herbert Wertheim School of Public Health and Human Longevity Science, University of California, 9500 Gilman Dr., 92093-0628, San Diego, La Jolla, CA, USA
| | - Jinyuan Liu
- Vanderbilt University, Department of Medicine, Nashville, USA
| | - Ravi Goyal
- Division of Infectious Diseases and Global Public Health, University of California San Diego, La Jolla, CA, USA
| | - Susan Little
- Division of Infectious Diseases and Global Public Health, University of California San Diego, La Jolla, CA, USA
| | - Xin Tu
- Division of Biostatistics and Bioinformatics Herbert Wertheim School of Public Health and Human Longevity Science, University of California, 9500 Gilman Dr., 92093-0628, San Diego, La Jolla, CA, USA
| | - Sanjay Mehta
- Veterans Affairs, San Diego Healthcare System, San Diego, CA, USA
| |
Collapse
|
2
|
Rich SN, Cook RL, Mavian CN, Garrett K, Spencer EC, Salemi M, Prosperi M. Network typologies predict future molecular linkages in the network of HIV transmission. AIDS 2023; 37:1739-1746. [PMID: 37289578 PMCID: PMC10399949 DOI: 10.1097/qad.0000000000003621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Revised: 05/30/2023] [Accepted: 06/02/2023] [Indexed: 06/10/2023]
Abstract
OBJECTIVE HIV molecular transmission network typologies have previously demonstrated associations to transmission risk; however, few studies have evaluated their predictive potential in anticipating future transmission events. To assess this, we tested multiple models on statewide surveillance data from the Florida Department of Health. DESIGN This was a retrospective, observational cohort study examining the incidence of new HIV molecular linkages within the existing molecular network of persons with HIV (PWH) in Florida. METHODS HIV-1 molecular transmission clusters were reconstructed for PWH diagnosed in Florida from 2006 to 2017 using the HIV-TRAnsmission Cluster Engine (HIV-TRACE). A suite of machine-learning models designed to predict linkage to a new diagnosis were internally and temporally externally validated using a variety of demographic, clinical, and network-derived parameters. RESULTS Of the 9897 individuals who received a genotype within 12 months of diagnosis during 2012-2017, 2611 (26.4%) were molecularly linked to another case within 1 year at 1.5% genetic distance. The best performing model, trained on two years of data, was high performing (area under the receiving operating curve = 0.96, sensitivity = 0.91, and specificity = 0.90) and included the following variables: age group, exposure group, node degree, betweenness, transitivity, and neighborhood. CONCLUSIONS In the molecular network of HIV transmission in Florida, individuals' network position and connectivity predicted future molecular linkages. Machine-learned models using network typologies performed superior to models using individual data alone. These models can be used to more precisely identify subpopulations for intervention.
Collapse
Affiliation(s)
- Shannan N. Rich
- Department of Epidemiology, Colleges of Public Health and Health Professions and Medicine
- Emerging Pathogens Institute
| | - Robert L. Cook
- Department of Epidemiology, Colleges of Public Health and Health Professions and Medicine
- Emerging Pathogens Institute
| | - Carla N. Mavian
- Emerging Pathogens Institute
- Department of Pathology, Immunology, and Laboratory Medicine, College of Medicine
| | - Karen Garrett
- Emerging Pathogens Institute
- Department of Plant Pathology, University of Florida, Gainesville
| | - Emma C. Spencer
- Florida Department of Health, Division of Disease Control and Health Protection, Bureau of Communicable Diseases, Tallahassee, Florida, USA
| | - Marco Salemi
- Emerging Pathogens Institute
- Department of Pathology, Immunology, and Laboratory Medicine, College of Medicine
| | - Mattia Prosperi
- Department of Epidemiology, Colleges of Public Health and Health Professions and Medicine
| |
Collapse
|
3
|
Dennis AM, Mobley V. Interrupting HIV transmission networks: how can we design and implement timely and effective interventions? Expert Rev Anti Infect Ther 2023; 21:691-693. [PMID: 37272332 PMCID: PMC10330925 DOI: 10.1080/14787210.2023.2221850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 06/01/2023] [Indexed: 06/06/2023]
Affiliation(s)
- Ann M. Dennis
- Division of Infectious Diseases, University of North Carolina at Chapel Hill
| | - Victoria Mobley
- Division of Public Health, Communicable Disease Branch, North Carolina Department of Health and Human Services
| |
Collapse
|
4
|
Didelot X, Franceschi V, Frost SDW, Dennis A, Volz EM. Model design for nonparametric phylodynamic inference and applications to pathogen surveillance. Virus Evol 2023; 9:vead028. [PMID: 37229349 PMCID: PMC10205094 DOI: 10.1093/ve/vead028] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 04/17/2023] [Accepted: 04/26/2023] [Indexed: 05/27/2023] Open
Abstract
Inference of effective population size from genomic data can provide unique information about demographic history and, when applied to pathogen genetic data, can also provide insights into epidemiological dynamics. The combination of nonparametric models for population dynamics with molecular clock models which relate genetic data to time has enabled phylodynamic inference based on large sets of time-stamped genetic sequence data. The methodology for nonparametric inference of effective population size is well-developed in the Bayesian setting, but here we develop a frequentist approach based on nonparametric latent process models of population size dynamics. We appeal to statistical principles based on out-of-sample prediction accuracy in order to optimize parameters that control shape and smoothness of the population size over time. Our methodology is implemented in a new R package entitled mlesky. We demonstrate the flexibility and speed of this approach in a series of simulation experiments and apply the methodology to a dataset of HIV-1 in the USA. We also estimate the impact of non-pharmaceutical interventions for COVID-19 in England using thousands of SARS-CoV-2 sequences. By incorporating a measure of the strength of these interventions over time within the phylodynamic model, we estimate the impact of the first national lockdown in the UK on the epidemic reproduction number.
Collapse
Affiliation(s)
- Xavier Didelot
- School of Life Sciences and Department of Statistics, University of Warwick, United Kingdom
| | - Vinicius Franceschi
- Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, United Kingdom
| | | | - Ann Dennis
- Department of Medicine, University of North Carolina, USA
| | - Erik M Volz
- Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, United Kingdom
| |
Collapse
|
5
|
Novitsky V, Steingrimsson J, Howison M, Dunn CW, Gillani FS, Fulton J, Bertrand T, Howe K, Bhattarai L, Ronquillo G, MacAskill M, Bandy U, Hogan J, Kantor R. Not all clusters are equal: dynamics of molecular HIV-1 clusters in a statewide Rhode Island epidemic. AIDS 2023; 37:389-399. [PMID: 36695355 PMCID: PMC9881752 DOI: 10.1097/qad.0000000000003426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
OBJECTIVES Molecular epidemiology is a powerful tool to characterize HIV epidemics and prioritize public health interventions. Typically, HIV clusters are assumed to have uniform patterns over time. We hypothesized that assessment of cluster evolution would reveal distinct cluster behavior, possibly improving molecular epidemic characterization, towards disrupting HIV transmission. DESIGN Retrospective cohort. METHODS Annual phylogenies were inferred by cumulative aggregation of all available HIV-1 pol sequences of individuals with HIV-1 in Rhode Island (RI) between 1990 and 2020, representing a statewide epidemic. Molecular clusters were detected in annual phylogenies by strict and relaxed cluster definition criteria, and the impact of annual newly-diagnosed HIV-1 cases to the structure of individual clusters was examined over time. RESULTS Of 2153 individuals, 31% (strict criteria) - 47% (relaxed criteria) clustered. Longitudinal tracking of individual clusters identified three cluster types: normal, semi-normal and abnormal. Normal clusters (83-87% of all identified clusters) showed predicted growing/plateauing dynamics, with approximately three-fold higher growth rates in large (15-18%) vs. small (∼5%) clusters. Semi-normal clusters (1-2% of all clusters) temporarily fluctuated in size and composition. Abnormal clusters (11-16% of all clusters) demonstrated collapses and re-arrangements over time. Borderline values of cluster-defining parameters explained dynamics of non-normal clusters. CONCLUSIONS Comprehensive tracing of molecular HIV clusters over time in a statewide epidemic identified distinct cluster types, likely missed in cross-sectional analyses, demonstrating that not all clusters are equal. This knowledge challenges current perceptions of consistent cluster behavior over time and could improve molecular surveillance of local HIV epidemics to better inform public health strategies.
Collapse
Affiliation(s)
| | | | - Mark Howison
- Research Improving People’s Lives, Providence, RI, USA
| | | | | | | | | | | | | | | | | | - Utpala Bandy
- Rhode Island Department of Health, Providence, RI, USA
| | | | | |
Collapse
|
6
|
Zhao B, Qiu Y, Song W, Kang M, Dong X, Li X, Wang L, Liu J, Ding H, Chu Z, Wang L, Tian W, Shang H, Han X. Undiagnosed HIV Infections May Drive HIV Transmission in the Era of "Treat All": A Deep-Sampling Molecular Network Study in Northeast China during 2016 to 2019. Viruses 2022; 14:v14091895. [PMID: 36146701 PMCID: PMC9502473 DOI: 10.3390/v14091895] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 08/24/2022] [Accepted: 08/24/2022] [Indexed: 11/23/2022] Open
Abstract
Universal antiretroviral therapy (ART, “treat all”) was recommended by the World Health Organization in 2015; however, HIV-1 transmission is still ongoing. This study characterizes the drivers of HIV transmission in the “treat all” era. Demographic and clinical information and HIV pol gene were collected from all newly diagnosed cases in Shenyang, the largest city in Northeast China, during 2016 to 2019. Molecular networks were constructed based on genetic distance and logistic regression analysis was used to assess potential transmission source characteristics. The cumulative ART coverage in Shenyang increased significantly from 77.0% (485/630) in 2016 to 93.0% (2598/2794) in 2019 (p < 0.001). Molecular networks showed that recent HIV infections linked to untreated individuals decreased from 61.6% in 2017 to 28.9% in 2019, while linking to individuals with viral suppression (VS) increased from 9.0% to 49.0% during the same time frame (p < 0.001). Undiagnosed people living with HIV (PLWH) hidden behind the links between index cases and individuals with VS were likely to be male, younger than 25 years of age, with Manchu nationality (p < 0.05). HIV transmission has declined significantly in the era of “treat all”. Undiagnosed PLWH may drive HIV transmission and should be the target for early detection and intervention.
Collapse
Affiliation(s)
- Bin Zhao
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Yu Qiu
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Wei Song
- Department of Food Safety and Nutrition, Shenyang Center for Health Service and Administrative Law Enforcement (Shenyang Center for Disease Control and Prevention), Shenyang 110031, China
| | - Mingming Kang
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Xue Dong
- Department of Food Safety and Nutrition, Shenyang Center for Health Service and Administrative Law Enforcement (Shenyang Center for Disease Control and Prevention), Shenyang 110031, China
| | - Xin Li
- Department of Food Safety and Nutrition, Shenyang Center for Health Service and Administrative Law Enforcement (Shenyang Center for Disease Control and Prevention), Shenyang 110031, China
| | - Lu Wang
- Department of Food Safety and Nutrition, Shenyang Center for Health Service and Administrative Law Enforcement (Shenyang Center for Disease Control and Prevention), Shenyang 110031, China
| | - Jianmin Liu
- Department of Food Safety and Nutrition, Shenyang Center for Health Service and Administrative Law Enforcement (Shenyang Center for Disease Control and Prevention), Shenyang 110031, China
| | - Haibo Ding
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Zhenxing Chu
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Lin Wang
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Wen Tian
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
| | - Hong Shang
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
- Correspondence: (H.S.); (X.H.); Tel./Fax: +86-(24)-8328-2634 (H.S. & X.H.)
| | - Xiaoxu Han
- NHC Key Laboratory of AIDS Immunology (China Medical University), National Clinical Research Center for Laboratory Medicine, The First Hospital of China Medical University, Shenyang 110001, China
- Laboratory Medicine Innovation Unit, Chinese Academy of Medical Sciences, Shenyang 110001, China
- Key Laboratory of AIDS Immunology of Liaoning Province, Shenyang 110001, China
- Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, 79 Qingchun Street, Hangzhou 310003, China
- Correspondence: (H.S.); (X.H.); Tel./Fax: +86-(24)-8328-2634 (H.S. & X.H.)
| |
Collapse
|
7
|
Blenkinsop A, Monod M, Sighem AV, Pantazis N, Bezemer D, Op de Coul E, van de Laar T, Fraser C, Prins M, Reiss P, de Bree GJ, Ratmann O. Estimating the potential to prevent locally acquired HIV infections in a UNAIDS Fast-Track City, Amsterdam. eLife 2022; 11:76487. [PMID: 35920649 PMCID: PMC9545569 DOI: 10.7554/elife.76487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 08/01/2022] [Indexed: 11/13/2022] Open
Abstract
Background: More than 300 cities including the city of Amsterdam in the Netherlands have joined the UNAIDS Fast-Track Cities initiative, committing to accelerate their HIV response and end the AIDS epidemic in cities by 2030. To support this commitment, we aimed to estimate the number and proportion of Amsterdam HIV infections that originated within the city, from Amsterdam residents. We also aimed to estimate the proportion of recent HIV infections during the 5-year period 2014–2018 in Amsterdam that remained undiagnosed. Methods: We located diagnosed HIV infections in Amsterdam using postcode data (PC4) at time of registration in the ATHENA observational HIV cohort, and used HIV sequence data to reconstruct phylogeographically distinct, partially observed Amsterdam transmission chains. Individual-level infection times were estimated from biomarker data, and used to date the phylogenetically observed transmission chains as well as to estimate undiagnosed proportions among recent infections. A Bayesian Negative Binomial branching process model was used to estimate the number, size, and growth of the unobserved Amsterdam transmission chains from the partially observed phylogenetic data. Results: Between 1 January 2014 and 1 May 2019, there were 846 HIV diagnoses in Amsterdam residents, of whom 516 (61%) were estimated to have been infected in 2014–2018. The rate of new Amsterdam diagnoses since 2014 (104 per 100,000) remained higher than the national rates excluding Amsterdam (24 per 100,000), and in this sense Amsterdam remained a HIV hotspot in the Netherlands. An estimated 14% [12–16%] of infections in Amsterdan MSM in 2014–2018 remained undiagnosed by 1 May 2019, and 41% [35–48%] in Amsterdam heterosexuals, with variation by region of birth. An estimated 67% [60–74%] of Amsterdam MSM infections in 2014–2018 had an Amsterdam resident as source, and 56% [41–70%] in Amsterdam heterosexuals, with heterogeneity by region of birth. Of the locally acquired infections, an estimated 43% [37–49%] were in foreign-born MSM, 41% [35–47%] in Dutch-born MSM, 10% [6–18%] in foreign-born heterosexuals, and 5% [2–9%] in Dutch-born heterosexuals. We estimate the majority of Amsterdam MSM infections in 2014–2018 originated in transmission chains that pre-existed by 2014. Conclusions: This combined phylogenetic, epidemiologic, and modelling analysis in the UNAIDS Fast-Track City Amsterdam indicates that there remains considerable potential to prevent HIV infections among Amsterdam residents through city-level interventions. The burden of locally acquired infection remains concentrated in MSM, and both Dutch-born and foreign-born MSM would likely benefit most from intensified city-level interventions. Funding: This study received funding as part of the H-TEAM initiative from Aidsfonds (project number P29701). The H-TEAM initiative is being supported by Aidsfonds (grant number: 2013169, P29701, P60803), Stichting Amsterdam Dinner Foundation, Bristol-Myers Squibb International Corp. (study number: AI424-541), Gilead Sciences Europe Ltd (grant number: PA-HIV-PREP-16-0024), Gilead Sciences (protocol numbers: CO-NL-276-4222, CO-US-276-1712, CO-NL-985-6195), and M.A.C AIDS Fund.
Collapse
Affiliation(s)
| | - Mélodie Monod
- Department of Mathematics, Imperial College London, London, United Kingdom
| | | | - Nikos Pantazis
- Department of Hygiene, Epidemiology and Medical Statistics, University of Athens, Athens, Greece
| | | | - Eline Op de Coul
- Center for Infectious Diseases Prevention and Control, National Institute for Public Health and the Environment (RIVM), Bilthoven, Netherlands
| | - Thijs van de Laar
- Department of Donor Medicine Research, Sanquin, Amsterdam, Netherlands
| | - Christophe Fraser
- Big Data Institute, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
| | - Maria Prins
- Academic Medical Center, Amsterdam, Netherlands
| | - Peter Reiss
- Department of Global Health, Amsterdam University Medical Centers, Amsterdam, Netherlands
| | - Godelieve J de Bree
- Department of Global Health, Amsterdam University Medical Centers, Amsterdam, Netherlands
| | - Oliver Ratmann
- Department of Mathematics, Imperial College London, London, United Kingdom
| |
Collapse
|