Article Text

Comprehensive compartmental model and calibration algorithm for the study of clinical implications of the population-level spread of COVID-19: a study protocol
  1. Brandon Robinson1,
  2. Jodi D Edwards2,3,
  3. Tetyana Kendzerska3,4,5,
  4. Chris L Pettit6,
  5. Dominique Poirel7,
  6. John M Daly8,
  7. Mehdi Ammi9,
  8. Mohammad Khalil10,
  9. Peter J Taillon11,
  10. Rimple Sandhu12,
  11. Shirley Mills13,
  12. Sunita Mulpuru4,5,
  13. Thomas Walker1,
  14. Valerie Percival14,
  15. Victorita Dolean15,16,
  16. Abhijit Sarkar1
  1. 1Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario, Canada
  2. 2School of Epidemiology and Public Health, University of Ottawa and University of Ottawa Heart Institute, Ottawa, Ontario, Canada
  3. 3ICES, Ottawa, Ontario, Canada
  4. 4The Ottawa Hospital Research Institute, Ottawa, Ontario, Canada
  5. 5Department of Medicine, Faculty of Medicine, Division of Respirology, University of Ottawa, Ottawa, Ontario, Canada
  6. 6US Naval Academy, Aerospace Engineering Department, Annapolis, Maryland, USA
  7. 7Royal Military College of Canada, Department of Mechanical and Aerospace Engineering, Kingston, Ontario, Canada
  8. 8Independent Control Systems Engineer, Ottawa, Ontario, Canada
  9. 9School of Public Policy and Administration, Carleton University, Ottawa, Ontario, Canada
  10. 10Sandia National Laboratories, Livermore, California, USA
  11. 11Schaffen Research Inc, Ottawa, Ontario, Canada
  12. 12National Renewable Energy Laboratory, Golden, Colorado, USA
  13. 13School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada
  14. 14School of International Affairs, Carleton University, Ottawa, Ontario, Canada
  15. 15Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland
  16. 16Laboratoire J.A. Dieudonné, CNRS, Université Côte d’Azur, Nice, France
  1. Correspondence to Professor Abhijit Sarkar; abhijit.sarkar{at}


Introduction The complex dynamics of the coronavirus disease 2019 (COVID-19) pandemic has made obtaining reliable long-term forecasts of the disease progression difficult. Simple mechanistic models with deterministic parameters are useful for short-term predictions but have ultimately been unsuccessful in extrapolating the trajectory of the pandemic because of unmodelled dynamics and the unrealistic level of certainty that is assumed in the predictions.

Methods and analysis We propose a 22-compartment epidemiological model that includes compartments not previously considered concurrently, to account for the effects of vaccination, asymptomatic individuals, inadequate access to hospital care, post-acute COVID-19 and recovery with long-term health complications. Additionally, new connections between compartments introduce new dynamics to the system and provide a framework to study the sensitivity of model outputs to several concurrent effects, including temporary immunity, vaccination rate and vaccine effectiveness. Subject to data availability for a given region, we discuss a means by which population demographics (age, comorbidity, socioeconomic status, sex and geographical location) and clinically relevant information (different variants, different vaccines) can be incorporated within the 22-compartment framework. Considering a probabilistic interpretation of the parameters allows the model’s predictions to reflect the current state of uncertainty about the model parameters and model states. We propose the use of a sparse Bayesian learning algorithm for parameter calibration and model selection. This methodology considers a combination of prescribed parameter prior distributions for parameters that are known to be essential to the modelled dynamics and automatic relevance determination priors for parameters whose relevance is questionable. This is useful as it helps prevent overfitting the available epidemiological data when calibrating the parameters of the proposed model. Population-level administrative health data will serve as partial observations of the model states.

Ethics and dissemination Approved by Carleton University’s Research Ethics Board-B (clearance ID: 114596). Results will be made available through future publication.

  • COVID-19
  • epidemiology
  • statistics & research methods

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  • Contributors BR drafted the protocol, derived the equations in the supplemental material and will conduct and report the research findings. JDE, TK and AS contributed substantially to the conception of the study. JDE, TK and SMulpuru provided clinical/epidemiological context. CLP, DP, MK, RS, JMD and TW contributed to the algorithmic development and implementation. JDE, TK and SMills contributed to the data acquisition and utilisation perspective. PJT and VD contributed to computational/software aspect. MA and VP provided critical insight on the role of modelling in public policy. All listed authors contributed to revision of the protocol for intellectual content and have approved the final version.

  • Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

  • Competing interests None declared.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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