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Earn DJD, Park SW, Bolker BM. Fitting Epidemic Models to Data: A Tutorial in Memory of Fred Brauer. Bull Math Biol 2024; 86:109. [PMID: 39052140 DOI: 10.1007/s11538-024-01326-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 06/04/2024] [Indexed: 07/27/2024]
Abstract
Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred's questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.
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Affiliation(s)
- David J D Earn
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada.
| | - Sang Woo Park
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, 08544, USA
| | - Benjamin M Bolker
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada
- Department of Biology, McMaster University, Hamilton, ON, L8S 4K1, Canada
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2
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Wani AK, Chopra C, Dhanjal DS, Akhtar N, Singh H, Bhau P, Singh A, Sharma V, Pinheiro RSB, Américo-Pinheiro JHP, Singh R. Metagenomics in the fight against zoonotic viral infections: A focus on SARS-CoV-2 analogues. J Virol Methods 2024; 323:114837. [PMID: 37914040 DOI: 10.1016/j.jviromet.2023.114837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 10/24/2023] [Accepted: 10/27/2023] [Indexed: 11/03/2023]
Abstract
Zoonotic viral infections continue to pose significant threats to global public health, as highlighted by the COVID-19 pandemic caused by the SARS-CoV-2 virus. The emergence of SARS-CoV-2 served as a stark reminder of the potential for zoonotic transmission of viruses from animals to humans. Understanding the origins and dynamics of zoonotic viruses is critical for early detection, prevention, and effective management of future outbreaks. Metagenomics has emerged as a powerful tool for investigating the virome of diverse ecosystems, shedding light on the diversity of viral populations, their hosts, and potential zoonotic spillover events. We provide an in-depth examination of metagenomic approaches, including, NGS metagenomics, shotgun metagenomics, viral metagenomics, and single-virus metagenomics, highlighting their strengths and limitations in identifying and characterizing zoonotic viral pathogens. This review underscores the pivotal role of metagenomics in enhancing our ability to detect, monitor, and mitigate zoonotic viral infections, using SARS-CoV-2 analogues as a case study. We emphasize the need for continued interdisciplinary collaboration among virologists, ecologists, and bioinformaticians to harness the full potential of metagenomic approaches in safeguarding public health against emerging zoonotic threats.
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Affiliation(s)
- Atif Khurshid Wani
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India
| | - Chirag Chopra
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India
| | - Daljeet Singh Dhanjal
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India
| | - Nahid Akhtar
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India
| | - Himanshu Singh
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India
| | - Poorvi Bhau
- School of Biotechnology, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, India
| | - Anjuvan Singh
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India
| | - Varun Sharma
- NMC Genetics India Pvt. Ltd, Gurugram, Harayana, India
| | - Rafael Silvio Bonilha Pinheiro
- School of Veterinary Medicine and Animal Science, Department of Animal Production, São Paulo State University (UNESP), Botucatu, SP, Brazil
| | - Juliana Heloisa Pinê Américo-Pinheiro
- Department of Forest Science, Soils and Environment, School of Agronomic Sciences, São Paulo State University (UNESP), Ave. Universitária, 3780, Botucatu, SP 18610-034, Brazil; Graduate Program in Environmental Sciences, Brazil University, Street Carolina Fonseca, 584, São Paulo, SP 08230-030, Brazil
| | - Reena Singh
- School of Bioengineering and Biosciences, Lovely Professional University, Punjab 144411, India.
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Klunk J, Vilgalys TP, Demeure CE, Cheng X, Shiratori M, Madej J, Beau R, Elli D, Patino MI, Redfern R, DeWitte SN, Gamble JA, Boldsen JL, Carmichael A, Varlik N, Eaton K, Grenier JC, Golding GB, Devault A, Rouillard JM, Yotova V, Sindeaux R, Ye CJ, Bikaran M, Dumaine A, Brinkworth JF, Missiakas D, Rouleau GA, Steinrücken M, Pizarro-Cerdá J, Poinar HN, Barreiro LB. Evolution of immune genes is associated with the Black Death. Nature 2022; 611:312-319. [PMID: 36261521 PMCID: PMC9580435 DOI: 10.1038/s41586-022-05349-x] [Citation(s) in RCA: 84] [Impact Index Per Article: 42.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 09/14/2022] [Indexed: 01/10/2023]
Abstract
Infectious diseases are among the strongest selective pressures driving human evolution1,2. This includes the single greatest mortality event in recorded history, the first outbreak of the second pandemic of plague, commonly called the Black Death, which was caused by the bacterium Yersinia pestis3. This pandemic devastated Afro-Eurasia, killing up to 30-50% of the population4. To identify loci that may have been under selection during the Black Death, we characterized genetic variation around immune-related genes from 206 ancient DNA extracts, stemming from two different European populations before, during and after the Black Death. Immune loci are strongly enriched for highly differentiated sites relative to a set of non-immune loci, suggesting positive selection. We identify 245 variants that are highly differentiated within the London dataset, four of which were replicated in an independent cohort from Denmark, and represent the strongest candidates for positive selection. The selected allele for one of these variants, rs2549794, is associated with the production of a full-length (versus truncated) ERAP2 transcript, variation in cytokine response to Y. pestis and increased ability to control intracellular Y. pestis in macrophages. Finally, we show that protective variants overlap with alleles that are today associated with increased susceptibility to autoimmune diseases, providing empirical evidence for the role played by past pandemics in shaping present-day susceptibility to disease.
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Affiliation(s)
- Jennifer Klunk
- McMaster Ancient DNA Centre, Departments of Anthropology, Biology and Biochemistry, McMaster University, Hamilton, Ontario, Canada
- Daicel Arbor Biosciences, Ann Arbor, MI, USA
| | - Tauras P Vilgalys
- Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, IL, USA
| | | | - Xiaoheng Cheng
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
| | - Mari Shiratori
- Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, IL, USA
| | - Julien Madej
- Yersinia Research Unit, Institut Pasteur, Paris, France
| | - Rémi Beau
- Yersinia Research Unit, Institut Pasteur, Paris, France
| | - Derek Elli
- Department of Microbiology, Ricketts Laboratory, University of Chicago, Lemont, IL, USA
| | - Maria I Patino
- Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, IL, USA
| | - Rebecca Redfern
- Centre for Human Bioarchaeology, Museum of London, London, UK
| | - Sharon N DeWitte
- Department of Anthropology, University of South Carolina, Columbia, SC, USA
| | - Julia A Gamble
- Department of Anthropology, University of Manitoba, Winnipeg, Manitoba, Canada
| | - Jesper L Boldsen
- Department of Forensic Medicine, Unit of Anthropology (ADBOU), University of Southern Denmark, Odense S, Denmark
| | - Ann Carmichael
- History Department, Indiana University, Bloomington, IN, USA
| | - Nükhet Varlik
- Department of History, Rutgers University, Newark, NJ, USA
| | - Katherine Eaton
- McMaster Ancient DNA Centre, Departments of Anthropology, Biology and Biochemistry, McMaster University, Hamilton, Ontario, Canada
| | - Jean-Christophe Grenier
- Montreal Heart Institute, Faculty of Medicine, Université de Montréal, Montréal, Quebec, Canada
| | - G Brian Golding
- McMaster Ancient DNA Centre, Departments of Anthropology, Biology and Biochemistry, McMaster University, Hamilton, Ontario, Canada
| | | | - Jean-Marie Rouillard
- Daicel Arbor Biosciences, Ann Arbor, MI, USA
- Department of Chemical Engineering, University of Michigan - Ann Arbor, Ann Arbor, MI, USA
| | - Vania Yotova
- Centre Hospitalier Universitaire Sainte-Justine, Montréal, Quebec, Canada
| | - Renata Sindeaux
- Centre Hospitalier Universitaire Sainte-Justine, Montréal, Quebec, Canada
| | - Chun Jimmie Ye
- Division of Rheumatology, Department of Medicine, University of California, San Francisco, CA, USA
- Institute for Human Genetics, University of California, San Francisco, CA, USA
| | - Matin Bikaran
- Division of Rheumatology, Department of Medicine, University of California, San Francisco, CA, USA
- Institute for Human Genetics, University of California, San Francisco, CA, USA
| | - Anne Dumaine
- Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, IL, USA
| | - Jessica F Brinkworth
- Department of Anthropology, University of Illinois Urbana-Champaign, Urbana, IL, USA
- Carl R Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Dominique Missiakas
- Department of Microbiology, Ricketts Laboratory, University of Chicago, Lemont, IL, USA
| | - Guy A Rouleau
- Montreal Neurological Institute-Hospital, McGill University, Montréal, Quebec, Canada
| | - Matthias Steinrücken
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
- Department of Human Genetics, University of Chicago, Chicago, IL, USA
| | | | - Hendrik N Poinar
- McMaster Ancient DNA Centre, Departments of Anthropology, Biology and Biochemistry, McMaster University, Hamilton, Ontario, Canada.
- Michael G. DeGroote Institute of Infectious Disease Research, McMaster University, Hamilton, Ontario, Canada.
- Humans and the Microbiome Program, Canadian Institute for Advanced Research, Toronto, Ontario, Canada.
| | - Luis B Barreiro
- Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, IL, USA.
- Department of Human Genetics, University of Chicago, Chicago, IL, USA.
- Committee on Genetics, Genomics, and Systems Biology, University of Chicago, Chicago, IL, USA.
- Committee on Immunology, University of Chicago, Chicago, IL, USA.
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4
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Hu Y, Wang K, Wang W. Analysis of the Geographic Transmission Differences of COVID-19 in China Caused by Population Movement and Population Density. Bull Math Biol 2022; 84:94. [PMID: 35913582 PMCID: PMC9340757 DOI: 10.1007/s11538-022-01050-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 07/04/2022] [Indexed: 11/29/2022]
Abstract
The coronavirus disease (COVID-19) has led to a global pandemic and caused huge healthy and economic losses. Non-pharmaceutical interventions, especially contact tracing and social distance restrictions, play a vital role in the control of COVID-19. Understanding the spatial impact is essential for designing such a control policy. Based on epidemic data of the confirmed cases after the Wuhan lockdown, we calculate the invasive reproduction numbers of COVID-19 in the different regions of China. Statistical analysis indicates a significant positive correlation between the reproduction numbers and the population input sizes from Wuhan, which indicates that the large-scale population movement contributed a lot to the geographic spread of COVID-19 in China. Moreover, there is a significant positive correlation between reproduction numbers and local population densities, which shows that the higher population density intensifies the spread of disease. Considering that in the early stage, there were sequential imported cases that affected the estimation of reproduction numbers, we classify the imported cases and local cases through the information of epidemiological data and calculate the net invasive reproduction number to quantify the local spread of the epidemic. The results are applied to the design of border control policy on the basis of vaccination coverage.
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Affiliation(s)
- Yi Hu
- School of mathematics and statistics, Southwest University, Chongqing, 400715, People's Republic of China
| | - Kaifa Wang
- School of mathematics and statistics, Southwest University, Chongqing, 400715, People's Republic of China
| | - Wendi Wang
- School of mathematics and statistics, Southwest University, Chongqing, 400715, People's Republic of China.
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Tao Y, Hite JL, Lafferty KD, Earn DJD, Bharti N. Transient disease dynamics across ecological scales. THEOR ECOL-NETH 2021; 14:625-640. [PMID: 34075317 PMCID: PMC8156581 DOI: 10.1007/s12080-021-00514-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 05/04/2021] [Indexed: 11/25/2022]
Abstract
Analyses of transient dynamics are critical to understanding infectious disease transmission and persistence. Identifying and predicting transients across scales, from within-host to community-level patterns, plays an important role in combating ongoing epidemics and mitigating the risk of future outbreaks. Moreover, greater emphases on non-asymptotic processes will enable timely evaluations of wildlife and human diseases and lead to improved surveillance efforts, preventive responses, and intervention strategies. Here, we explore the contributions of transient analyses in recent models spanning the fields of epidemiology, movement ecology, and parasitology. In addition to their roles in predicting epidemic patterns and endemic outbreaks, we explore transients in the contexts of pathogen transmission, resistance, and avoidance at various scales of the ecological hierarchy. Examples illustrate how (i) transient movement dynamics at the individual host level can modify opportunities for transmission events over time; (ii) within-host energetic processes often lead to transient dynamics in immunity, pathogen load, and transmission potential; (iii) transient connectivity between discrete populations in response to environmental factors and outbreak dynamics can affect disease spread across spatial networks; and (iv) increasing species richness in a community can provide transient protection to individuals against infection. Ultimately, we suggest that transient analyses offer deeper insights and raise new, interdisciplinary questions for disease research, consequently broadening the applications of dynamical models for outbreak preparedness and management. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s12080-021-00514-w.
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Affiliation(s)
- Yun Tao
- Intelligence Community Postdoctoral Research Fellowship Program, Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, CA 93106 USA
| | - Jessica L. Hite
- School of Veterinary Medicine, Department of Pathobiological Sciences, University of Wisconsin, Madison, WI 53706 USA
| | - Kevin D. Lafferty
- Western Ecological Research Center at UCSB Marine Science Institute, U.S. Geological Survey, CA 93106 Santa Barbara, USA
| | - David J. D. Earn
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1 Canada
| | - Nita Bharti
- Department of Biology Center for Infectious Disease Dynamics, Penn State University, University Park, PA 16802 USA
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