Mathematics of Public Health

1. Front Matter

   Pages i-x

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2. Diverse Local Epidemics Reveal the Distinct Effects of Population Density, Demographics, Climate, Depletion of Susceptibles, and Intervention in the First Wave of COVID-19 in the United States

   • Niayesh Afshordi, Benjamin P. Holder, Mohammad Bahrami, Daniel Lichtblau

   Pages 1-23

3. Describing, Modelling and Forecasting the Spatial and Temporal Spread of COVID-19: A Short Review

   • Julien Arino

   Pages 25-51

4. A Logistic Growth Model with Logistically Varying Carrying Capacity for Covid-19 Deaths Using Data from Ontario, Canada

   • Georges Bucyibaruta, C. B. Dean, E. M. Renouf

   Pages 53-65

5. COVID-19 in Ontario: Modelling the Pandemic by Age Groups Incorporating Preventative Rapid-Testing

   • Roie Fields, Lia Humphrey, Edward W. Thommes, Monica G. Cojocaru

   Pages 67-83

6. Sub-epidemic Model Forecasts During the First Wave of the COVID-19 Pandemic in the USA and European Hotspots

   • Gerardo Chowell, Richard Rothenberg, Kimberlyn Roosa, Amna Tariq, James M. Hyman, Ruiyan Luo

   Pages 85-137

7. A Model on the Large Scale Use of Convalescent Plasma to Treat Patients with Severe Symptoms

   • Xi Huo

   Pages 139-151

8. Generalized Additive Models to Capture the Death Rates in Canada COVID-19

   • Farzali Izadi

   Pages 153-171

9. Real-Time Prediction of the End of an Epidemic Wave: COVID-19 in China as a Case-Study

   • Quentin Griette, Zhihua Liu, Pierre Magal, Robin N. Thompson

   Pages 173-195

10. The Effect of Heterogeneity in Social Distancing on the Infection Peak for COVID-19

    • Connell McCluskey

    Pages 197-212

11. Forecasting Demand for Personal Protective Equipment for Ontario Acute Care Hospitals During the First Wave of the COVID-19 Pandemic

    • Kali Barrett, Yoshiko Nakamachi, Terra Ierasts, Yasin A. Khan, Stephen Mac, David Naimark et al.

    Pages 213-233

12. Don’t Wait, Re-escalate: Delayed Action Results in Longer Duration of COVID-19 Restrictions

    • Amy Hurford, James Watmough

    Pages 235-249

13. Learning COVID-19 Mitigation Strategies Using Reinforcement Learning

    • Nicholas Denis, Alexander El-Hajj, Blair Drummond, Yamina Abiza, Krishna Chaitanya Gopaluni

    Pages 251-271

14. Joint Modeling of Hospitalization and Mortality of Ontario Covid-19 Cases

    • Dexen D. Z. Xi, C. B. Dean, E. M. Renouf

    Pages 273-285

15. Evaluating the Risk of Reopening the Border: A Case Study of Ontario (Canada) to New York (USA) Using Mathematical Modeling

    • Pei Yuan, Elena Aruffo, Qi Li, Juan Li, Yi Tan, Tingting Zheng et al.

    Pages 287-301

16. Optimal Staged Reopening Schedule Based on ICU Capacity: A Model-Informed Strategy

    • Kyeongah Nah, Michael Chen, Ali Asgary, Zachary McCarthy, Francesca Scarabel, Yanyu Xiao et al.

    Pages 303-321

17. Mathematics of the Pandemic

    • M. Ram Murty, V. Kumar Murty

    Pages 323-353

Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research. This work brings together experts in mathematical modelling from across Canada and the world, presenting the latest modelling methods as they relate to the COVID-19 pandemic. 

A primary aim of this book is to make the content accessible so that researchers share the core methods that may be applied elsewhere. The mathematical theories and technologies in this book can be used to support decision makers on critical issues such as projecting outbreak trajectories, evaluating public health interventions for infection prevention and control, developing optimal strategies to return to a new normal, and designing vaccine candidates and informing mass immunization program.

Topical coverage includes: basic susceptible-exposed-infectious-recovered (SEIR) modelling framework modified and applied to COVID-19 disease transmission dynamics; nearcasting and forecasting for needs of critical medical resources including  personal protective equipment (PPE); predicting COVID-19 mortality; evaluating effectiveness of convalescent plasma treatment and the logistic implementation challenges; estimating impact of delays in contact tracing; quantifying heterogeneity in contact mixing and its evaluation with social distancing; modelling point of care diagnostics of COVID-19; and understanding non-reporting and underestimation.

Further, readers will have the opportunity to learn about current modelling methodologies and technologies for emerging infectious disease outbreaks, pandemic mitigation rapid response, and the mathematics behind them. The volume will help the general audience and experts to better understand the important role that mathematics has been playing during this on-going crisis in supporting critical decision-making by governments and public health agencies.

• Fields math modelling taskforce
• COVID-19 pandemic research
• mathematical methods COVID-19
• COVID-19 outbreak trajectories
• SEIR modeling
• transmission dynamics
• nearcasting COVID-19
• forecasting COVID-19
• plasma treatment COVID-19
• control measures
• reported and unreported cases
• regression analysis
• semi-parametric models
• generalized linear models
• generalized additive models
• statistical analysis
• data modeling
• link functions
• intermediate rank spline
• optimization

• Fields Institute for Research in Mathematical Sciences, Toronto, Canada

  V. Kumar Murty

• Department of Mathematics and Statistics, York University, Toronto, Canada

  Jianhong Wu

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