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Northrup GR, White A, Parratt SR, Rozins C, Laine AL, Boots M. The evolutionary dynamics of hyperparasites. J Theor Biol 2024; 582:111741. [PMID: 38280543 DOI: 10.1016/j.jtbi.2024.111741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 12/14/2023] [Accepted: 01/16/2024] [Indexed: 01/29/2024]
Abstract
Evolutionary theory has typically focused on pairwise interactions, such as those between hosts and parasites, with relatively little work having been carried out on more complex interactions including hyperparasites: parasites of parasites. Hyperparasites are common in nature, with the chestnut blight fungus virus CHV-1 a well-known natural example, but also notably include the phages of important human bacterial diseases. We build a general modeling framework for the evolution of hyperparasites that highlights the central role that the ability of a hyperparasite to be transmitted with its parasite plays in their evolution. A key result is that hyperparasites which transmit with their parasite hosts (hitchhike) will be selected for lower virulence, trending towards hypermutualism or hypercommensalism. We examine the impact on the evolution of hyperparasite systems of a wide range of host and parasite traits showing, for example, that high parasite virulence selects for higher hyperparasite virulence resulting in reductions in parasite virulence when hyperparasitized. Furthermore, we show that acute parasite infection will also select for increased hyperparasite virulence. Our results have implications for hyperparasite research, both as biocontrol agents and for their role in shaping community ecology and evolution and moreover emphasize the importance of understanding evolution in the context of multitrophic interactions.
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Affiliation(s)
- Graham R Northrup
- Center for Computational Biology, College of Engineering, University of California, Berkeley, CA, USA.
| | - Andy White
- Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK; Department of Mathematics, Heriot-Watt University, Edinburgh, UK
| | - Steven R Parratt
- Department of Ecology, Evolution and Behaviour, University of Liverpool, Liverpool, UK
| | - Carly Rozins
- Department of Science and Technology Studies, Division of Natural Science, York University, Toronto, Ontario, Canada
| | - Anna-Liisa Laine
- Research Centre for Ecological Change, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Finland; Department of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland
| | - Mike Boots
- Department of Integrative Biology, University of California Berkeley, CA, USA; Center for Ecology and Conservation, College of Life and Environmental Sciences, University of Exeter, Penryn Campus, UK
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Brook CE, Northrup GR, Ehrenberg AJ, Doudna JA, Boots M. Optimizing COVID-19 control with asymptomatic surveillance testing in a university environment. Epidemics 2021; 37:100527. [PMID: 34814094 PMCID: PMC8591900 DOI: 10.1016/j.epidem.2021.100527] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Revised: 10/26/2021] [Accepted: 11/12/2021] [Indexed: 12/13/2022] Open
Abstract
The high proportion of transmission events derived from asymptomatic or presymptomatic infections make SARS-CoV-2, the causative agent in COVID-19, difficult to control through the traditional non-pharmaceutical interventions (NPIs) of symptom-based isolation and contact tracing. As a consequence, many US universities developed asymptomatic surveillance testing labs, to augment NPIs and control outbreaks on campus throughout the 2020-2021 academic year (AY); several of those labs continue to support asymptomatic surveillance efforts on campus in AY2021-2022. At the height of the pandemic, we built a stochastic branching process model of COVID-19 dynamics at UC Berkeley to advise optimal control strategies in a university environment. Our model combines behavioral interventions in the form of group size limits to deter superspreading, symptom-based isolation, and contact tracing, with asymptomatic surveillance testing. We found that behavioral interventions offer a cost-effective means of epidemic control: group size limits of six or fewer greatly reduce superspreading, and rapid isolation of symptomatic infections can halt rising epidemics, depending on the frequency of asymptomatic transmission in the population. Surveillance testing can overcome uncertainty surrounding asymptomatic infections, with the most effective approaches prioritizing frequent testing with rapid turnaround time to isolation over test sensitivity. Importantly, contact tracing amplifies population-level impacts of all infection isolations, making even delayed interventions effective. Combination of behavior-based NPIs and asymptomatic surveillance also reduces variation in daily case counts to produce more predictable epidemics. Furthermore, targeted, intensive testing of a minority of high transmission risk individuals can effectively control the COVID-19 epidemic for the surrounding population. Even in some highly vaccinated university settings in AY2021-2022, asymptomatic surveillance testing offers an effective means of identifying breakthrough infections, halting onward transmission, and reducing total caseload. We offer this blueprint and easy-to-implement modeling tool to other academic or professional communities navigating optimal return-to-work strategies.
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Affiliation(s)
- Cara E Brook
- Department of Integrative Biology, University of California, Berkeley, United States; Department of Ecology and Evolution, University of Chicago, United States.
| | - Graham R Northrup
- Center for Computational Biology, College of Engineering, University of California, Berkeley, United States
| | - Alexander J Ehrenberg
- Department of Integrative Biology, University of California, Berkeley, United States; Innovative Genomics Institute, University of California, Berkeley, United States; Helen Wills Neuroscience Institute, University of California, Berkeley, United States; Memory and Aging Center, Weill Institute for Neurosciences, University of California, San Francisco, United States
| | - Jennifer A Doudna
- Innovative Genomics Institute, University of California, Berkeley, United States; Department of Molecular and Cell Biology, University of California, Berkeley, United States; College of Chemistry, University of California, Berkeley, United States; J. David Gladstone Institutes, San Francisco, CA, United States; Howard Hughes Medical Institute, University of California, Berkeley, United States; California Institute for Quantitative Biosciences (QB3), University of California, Berkeley, Berkeley, CA, USA; MBIB Division, Lawrence Berkeley National Laboratory, Berkeley, Berkeley, CA, USA; Gladstone-UCSF Institute of Genomic Immunology, San Francisco, CA, USA
| | - Mike Boots
- Department of Integrative Biology, University of California, Berkeley, United States; Department of Biosciences, University of Exeter, Penryn, UK
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Brook CE, Northrup GR, Ehrenberg AJ, Doudna JA, Boots M. Optimizing COVID-19 control with asymptomatic surveillance testing in a university environment. medRxiv 2021:2020.11.12.20230870. [PMID: 33442708 PMCID: PMC7805470 DOI: 10.1101/2020.11.12.20230870] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The high proportion of transmission events derived from asymptomatic or presymptomatic infections make SARS-CoV-2, the causative agent in COVID-19, difficult to control through the traditional non-pharmaceutical interventions (NPIs) of symptom-based isolation and contact tracing. As a consequence, many US universities developed asymptomatic surveillance testing labs, to augment NPIs and control outbreaks on campus throughout the 2020-2021 academic year (AY); several of those labs continue to support asymptomatic surveillance efforts on campus in AY2021-2022. At the height of the pandemic, we built a stochastic branching process model of COVID-19 dynamics at UC Berkeley to advise optimal control strategies in a university environment. Our model combines behavioral interventions in the form of group size limits to deter superspreading, symptom-based isolation, and contact tracing, with asymptomatic surveillance testing. We found that behavioral interventions offer a cost-effective means of epidemic control: group size limits of six or fewer greatly reduce superspreading, and rapid isolation of symptomatic infections can halt rising epidemics, depending on the frequency of asymptomatic transmission in the population. Surveillance testing can overcome uncertainty surrounding asymptomatic infections, with the most effective approaches prioritizing frequent testing with rapid turnaround time to isolation over test sensitivity. Importantly, contact tracing amplifies population-level impacts of all infection isolations, making even delayed interventions effective. Combination of behavior-based NPIs and asymptomatic surveillance also reduces variation in daily case counts to produce more predictable epidemics. Furthermore, targeted, intensive testing of a minority of high transmission risk individuals can effectively control the COVID-19 epidemic for the surrounding population. Even in some highly vaccinated university settings in AY2021-2022, asymptomatic surveillance testing offers an effective means of identifying breakthrough infections, halting onward transmission, and reducing total caseload. We offer this blueprint and easy-to-implement modeling tool to other academic or professional communities navigating optimal return-to-work strategies.
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Affiliation(s)
- Cara E. Brook
- Department of Integrative Biology, University of California,
Berkeley
- Department of Ecology and Evolution, University of Chicago
| | - Graham R. Northrup
- Center for Computational Biology, College of Engineering,
University of California, Berkeley
| | - Alexander J. Ehrenberg
- Department of Integrative Biology, University of California,
Berkeley
- Innovative Genomics Institute, University of California,
Berkeley
- Helen Wills Neuroscience Institute, University of California,
Berkeley
- Memory and Aging Center, Weill Institute for Neurosciences,
University of California, San Francisco
| | | | - Jennifer A. Doudna
- Innovative Genomics Institute, University of California,
Berkeley
- Department of Molecular and Cell Biology, University of
California, Berkeley
- College of Chemistry, University of California, Berkeley
- J. David Gladstone Institutes, San Francisco, CA
- Howard Hughes Medical Institute, University of California,
Berkeley
| | - Mike Boots
- Department of Integrative Biology, University of California,
Berkeley
- Department of Biosciences, University of Exeter, Penryn,
UK
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Head JR, Andrejko KL, Cheng Q, Collender PA, Phillips S, Boser A, Heaney AK, Hoover CM, Wu SL, Northrup GR, Click K, Bardach NS, Lewnard JA, Remais JV. School closures reduced social mixing of children during COVID-19 with implications for transmission risk and school reopening policies. J R Soc Interface 2021; 18:20200970. [PMID: 33849340 PMCID: PMC8086933 DOI: 10.1098/rsif.2020.0970] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 03/24/2021] [Indexed: 12/14/2022] Open
Abstract
School closures may reduce the size of social networks among children, potentially limiting infectious disease transmission. To estimate the impact of K-12 closures and reopening policies on children's social interactions and COVID-19 incidence in California's Bay Area, we collected data on children's social contacts and assessed implications for transmission using an individual-based model. Elementary and Hispanic children had more contacts during closures than high school and non-Hispanic children, respectively. We estimated that spring 2020 closures of elementary schools averted 2167 cases in the Bay Area (95% CI: -985, 5572), fewer than middle (5884; 95% CI: 1478, 11.550), high school (8650; 95% CI: 3054, 15 940) and workplace (15 813; 95% CI: 9963, 22 617) closures. Under assumptions of moderate community transmission, we estimated that reopening for a four-month semester without any precautions will increase symptomatic illness among high school teachers (an additional 40.7% expected to experience symptomatic infection, 95% CI: 1.9, 61.1), middle school teachers (37.2%, 95% CI: 4.6, 58.1) and elementary school teachers (4.1%, 95% CI: -1.7, 12.0). However, we found that reopening policies for elementary schools that combine universal masking with classroom cohorts could result in few within-school transmissions, while high schools may require masking plus a staggered hybrid schedule. Stronger community interventions (e.g. remote work, social distancing) decreased the risk of within-school transmission across all measures studied, with the influence of community transmission minimized as the effectiveness of the within-school measures increased.
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Affiliation(s)
- Jennifer R. Head
- Division of Epidemiology, School of Public Health, University of California, Berkeley, CA, USA
| | - Kristin L. Andrejko
- Division of Epidemiology, School of Public Health, University of California, Berkeley, CA, USA
| | - Qu Cheng
- Division of Environmental Health Sciences, School of Public Health, University of California, Berkeley, CA, USA
| | - Philip A. Collender
- Division of Environmental Health Sciences, School of Public Health, University of California, Berkeley, CA, USA
| | - Sophie Phillips
- College of Letters and Science, University of California, Berkeley, CA, USA
| | - Anna Boser
- College of Letters and Science, University of California, Berkeley, CA, USA
| | - Alexandra K. Heaney
- Division of Environmental Health Sciences, School of Public Health, University of California, Berkeley, CA, USA
| | - Christopher M. Hoover
- Division of Environmental Health Sciences, School of Public Health, University of California, Berkeley, CA, USA
| | - Sean L. Wu
- Division of Epidemiology, School of Public Health, University of California, Berkeley, CA, USA
| | - Graham R. Northrup
- Center for Computational Biology, College of Engineering, University of California, Berkeley, CA, USA
| | - Karen Click
- Division of Epidemiology, School of Public Health, University of California, Berkeley, CA, USA
| | - Naomi S. Bardach
- Department of Pediatrics, School of Medicine, University of California, San Francisco, CA, USA
| | - Joseph A. Lewnard
- Division of Epidemiology, School of Public Health, University of California, Berkeley, CA, USA
- Center for Computational Biology, College of Engineering, University of California, Berkeley, CA, USA
- Division of Infectious Diseases and Vaccinology, School of Public Health, University of California, Berkeley, CA, USA
| | - Justin V. Remais
- College of Letters and Science, University of California, Berkeley, CA, USA
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Northrup GR, Qian L, Bruxvoort K, Marx FM, Whittles LK, Lewnard JA. Inference of Naturally Acquired Immunity Using a Self-matched Negative-Control Design. Epidemiology 2021; 32:168-178. [PMID: 33337670 PMCID: PMC7850593 DOI: 10.1097/ede.0000000000001305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2020] [Accepted: 11/17/2020] [Indexed: 11/25/2022]
Abstract
Host adaptive immune responses may protect against infection or disease when a pathogen is repeatedly encountered. The hazard ratio of infection or disease, given previous infection, is typically sought to estimate the strength of protective immunity. However, variation in individual exposure or susceptibility to infection may introduce frailty bias, whereby a tendency for infections to recur among individuals with greater risk confounds the causal association between previous infection and susceptibility. We introduce a self-matched "case-only" inference method to control for unmeasured individual heterogeneity, making use of negative-control endpoints not attributable to the pathogen of interest. To control for confounding, this method compares event times for endpoints due to the pathogen of interest and negative-control endpoints during counterfactual risk periods, defined according to individuals' infection history. We derive a standard Mantel-Haenszel (matched) odds ratio conveying the effect of prior infection on time to recurrence. We compare performance of this approach to several proportional hazards modeling frameworks and estimate statistical power of the proposed strategy under various conditions. In an example application, we use the proposed method to reestimate naturally acquired protection against rotavirus gastroenteritis using data from previously published cohort studies. This self-matched negative-control design may present a flexible alternative to existing approaches for analyzing naturally acquired immunity, as well as other exposures affecting the distribution of recurrent event times.
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Affiliation(s)
- Graham R. Northrup
- From the Center for Computational Biology, College of Engineering, University of California, Berkeley, Berkeley, CA
| | - Lei Qian
- Department of Research and Evaluation, Kaiser Permanente Southern California, Pasadena, CA
| | - Katia Bruxvoort
- Department of Research and Evaluation, Kaiser Permanente Southern California, Pasadena, CA
| | - Florian M. Marx
- Department of Paediatrics and Child Health, Faculty of Medicine and Health Sciences, Desmond Tutu Tuberculosis Centre, Stellenbosch University, Cape Town, South Africa
- DST-NRF South African Centre of Excellence and Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch, South Africa
| | - Lilith K. Whittles
- Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, London, United Kingdom
- MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, United Kingdom
- NIHR Health Protection Research Unit in Modelling Methodology, School of Public Health, Imperial College London, London, United Kingdom
| | - Joseph A. Lewnard
- From the Center for Computational Biology, College of Engineering, University of California, Berkeley, Berkeley, CA
- Division of Epidemiology, School of Public Health, University of California, Berkeley, Berkeley, CA
- Division of Infectious Diseases and Vaccinology, School of Public Health, University of California, Berkeley, Berkeley, CA
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Head JR, Andrejko K, Cheng Q, Collender PA, Phillips S, Boser A, Heaney AK, Hoover CM, Wu SL, Northrup GR, Click K, Harrison R, Lewnard JA, Remais JV. The effect of school closures and reopening strategies on COVID-19 infection dynamics in the San Francisco Bay Area: a cross-sectional survey and modeling analysis. medRxiv 2020:2020.08.06.20169797. [PMID: 32793934 PMCID: PMC7418765 DOI: 10.1101/2020.08.06.20169797] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
Abstract
Background Large-scale school closures have been implemented worldwide to curb the spread of COVID-19. However, the impact of school closures and re-opening on epidemic dynamics remains unclear. Methods We simulated COVID-19 transmission dynamics using an individual-based stochastic model, incorporating social-contact data of school-aged children during shelter-in-place orders derived from Bay Area (California) household surveys. We simulated transmission under observed conditions and counterfactual intervention scenarios between March 17-June 1, and evaluated various fall 2020 K-12 reopening strategies. Findings Between March 17-June 1, assuming children <10 were half as susceptible to infection as older children and adults, we estimated school closures averted a similar number of infections (13,842 cases; 95% CI: 6,290, 23,040) as workplace closures (15,813; 95% CI: 9,963, 22,617) and social distancing measures (7,030; 95% CI: 3,118, 11,676). School closure effects were driven by high school and middle school closures. Under assumptions of moderate community transmission, we estimate that fall 2020 school reopenings will increase symptomatic illness among high school teachers (an additional 40.7% expected to experience symptomatic infection, 95% CI: 1.9, 61.1), middle school teachers (37.2%, 95% CI: 4.6, 58.1), and elementary school teachers (4.1%, 95% CI: -1.7, 12.0). Results are highly dependent on uncertain parameters, notably the relative susceptibility and infectiousness of children, and extent of community transmission amid re-opening. The school-based interventions needed to reduce the risk to fewer than an additional 1% of teachers infected varies by grade level. A hybrid-learning approach with halved class sizes of 10 students may be needed in high schools, while maintaining small cohorts of 20 students may be needed for elementary schools. Interpretation Multiple in-school intervention strategies and community transmission reductions, beyond the extent achieved to date, will be necessary to avoid undue excess risk associated with school reopening. Policymakers must urgently enact policies that curb community transmission and implement within-school control measures to simultaneously address the tandem health crises posed by COVID-19 and adverse child health and development consequences of long-term school closures.
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Lewnard JA, Liu VX, Jackson ML, Schmidt MA, Jewell BL, Flores JP, Jentz C, Northrup GR, Mahmud A, Reingold AL, Petersen M, Jewell NP, Young S, Bellows J. Incidence, clinical outcomes, and transmission dynamics of severe coronavirus disease 2019 in California and Washington: prospective cohort study. BMJ 2020; 369:m1923. [PMID: 32444358 PMCID: PMC7243800 DOI: 10.1136/bmj.m1923] [Citation(s) in RCA: 128] [Impact Index Per Article: 32.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 05/12/2020] [Indexed: 01/08/2023]
Abstract
OBJECTIVE To understand the epidemiology and burden of severe coronavirus disease 2019 (covid-19) during the first epidemic wave on the west coast of the United States. DESIGN Prospective cohort study. SETTING Kaiser Permanente integrated healthcare delivery systems serving populations in northern California, southern California, and Washington state. PARTICIPANTS 1840 people with a first acute hospital admission for confirmed covid-19 by 22 April 2020, among 9 596 321 healthcare plan enrollees. Analyses of hospital length of stay and clinical outcomes included 1328 people admitted by 9 April 2020 (534 in northern California, 711 in southern California, and 83 in Washington). MAIN OUTCOME MEASURES Cumulative incidence of first acute hospital admission for confirmed covid-19, and subsequent probabilities of admission to an intensive care unit (ICU) and mortality, as well as duration of hospital stay and ICU stay. The effective reproduction number (RE ) describing transmission dynamics was estimated for each region. RESULTS As of 22 April 2020, cumulative incidences of a first acute hospital admission for covid-19 were 15.6 per 100 000 cohort members in northern California, 23.3 per 100 000 in southern California, and 14.7 per 100 000 in Washington. Accounting for censoring of incomplete hospital stays among those admitted by 9 April 2020, the estimated median duration of stay among survivors was 9.3 days (with 95% staying 0.8 to 32.9 days) and among non-survivors was 12.7 days (1.6 to 37.7 days). The censoring adjusted probability of ICU admission for male patients was 48.5% (95% confidence interval 41.8% to 56.3%) and for female patients was 32.0% (26.6% to 38.4%). For patients requiring critical care, the median duration of ICU stay was 10.6 days (with 95% staying 1.3 to 30.8 days). The censoring adjusted case fatality ratio was 23.5% (95% confidence interval 19.6% to 28.2%) among male inpatients and 14.9% (11.8% to 18.6%) among female inpatients; mortality risk increased with age for both male and female patients. Reductions in RE were identified over the study period within each region. CONCLUSIONS Among residents of California and Washington state enrolled in Kaiser Permanente healthcare plans who were admitted to hospital with covid-19, the probabilities of ICU admission, of long hospital stay, and of mortality were identified to be high. Incidence rates of new hospital admissions have stabilized or declined in conjunction with implementation of social distancing interventions.
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Affiliation(s)
- Joseph A Lewnard
- Division of Epidemiology and Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, CA, 94720, USA
- Division of Infectious Diseases and Vaccinology, School of Public Health, University of California, Berkeley, Berkeley, CA, USA
- Center for Computational Biology, College of Engineering, University of California, Berkeley, Berkeley, CA, USA
| | - Vincent X Liu
- Division of Research, Kaiser Permanente, Oakland, CA, USA
| | - Michael L Jackson
- Health Research Institute, Kaiser Permanente Washington, Seattle, WA, USA
| | - Mark A Schmidt
- Center for Health Research, Kaiser Permanente Northwest, Portland, OR, USA
| | - Britta L Jewell
- MRC Centre for Global Infectious Disease Analysis, Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London, London, UK
- Department of Infectious Disease Epidemiology, Imperial College London, London, UK
| | - Jean P Flores
- The Care Management Institute, Kaiser Permanente, Oakland, California 94612
| | - Chris Jentz
- The Care Management Institute, Kaiser Permanente, Oakland, California 94612
| | - Graham R Northrup
- Center for Computational Biology, College of Engineering, University of California, Berkeley, Berkeley, CA, USA
| | - Ayesha Mahmud
- Department of Demography, University of California, Berkeley, Berkeley, CA, USA
| | - Arthur L Reingold
- Division of Epidemiology and Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, CA, 94720, USA
| | - Maya Petersen
- Division of Epidemiology and Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, CA, 94720, USA
| | - Nicholas P Jewell
- Division of Epidemiology and Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, CA, 94720, USA
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK
| | - Scott Young
- The Care Management Institute, Kaiser Permanente, Oakland, California 94612
- The Permanente Federation, Kaiser Permanente, Oakland, CA, USA
| | - Jim Bellows
- The Care Management Institute, Kaiser Permanente, Oakland, California 94612
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