Challenges in Modeling SARS-CoV-2: Bridging the Best of Both Worlds Between Models and Reality Michael Li - McMaster University mcmaster.ca |
Background Math and Statistics MacTheoBio Theoretical, statistical and computational approaches to study biology Infectious diseases Spatial ecology Evolution mcmaster.ca June 26, 2020 | 2
Background Math and Statistics MacTheoBio Theoretical, statistical and computational approaches to study biology Infectious diseases Malaria Ebola Influenza Canine Rabies HIV etc.. mcmaster.ca June 26, 2020 | 3
Background Math and Statistics MacTheoBio Theoretical, statistical and computational approaches to study biology Infectious diseases Malaria Ebola Influenza Canine Rabies HIV etc.. I can read Chinese! mcmaster.ca June 26, 2020 | 4
2019–2020 Part 1 WuHan Novel Corona Virus Outbreak mcmaster.ca June 26, 2020 | 5
Background 2019–2020 WuHan Novel Corona Virus Outbreak Late December 2019, several • suspicious cases of pneumonia in Wuhan City, Hubei Province of China. Unknown virus • Early January 2020, Chinese • authorities confirmed that they had identified a new virus. mcmaster.ca June 26, 2020 | 6
Data collection Jan 21st 24:00 105 new cases, 3 discharge and 3 death 375 Cumulative cases 28 Discharged 9 death mcmaster.ca June 26, 2020 | 7
The Basic Reproductive Number/Ratio (R 0 ) Expected number of new cases per case • Good index of risk at the population level • mcmaster.ca June 26, 2020 | 8
The Basic Reproductive Number/Ratio (R 0 ) Expected number of new cases per case • Good index of risk at the population level • M ost V aluable P iece of information in disease modelling mcmaster.ca June 26, 2020 | 9
WH outbreak R 0 Estimates Majumder, M.S. and Mandl, K.D., 2020. Early in the epidemic: impact of preprints on global discourse about COVID-19 transmissibility. The Lancet Global Health, 8(5), pp.e627-e630. mcmaster.ca June 26, 2020 | 10
Exponential Fitting Framework • Exponential growth rate (r) • Generation Interval mcmaster.ca June 26, 2020 | 11
Exponential Fitting Framework • Exponential growth rate (r) • Generation Interval mcmaster.ca June 26, 2020 | 12
Exponential growth rate (r) Estimate from time series • data mcmaster.ca June 26, 2020 | 13
Exponential growth rate (r) Estimate from time series • data mcmaster.ca June 26, 2020 | 14
Exponential growth rate (r) Estimate from time series • X data mcmaster.ca June 26, 2020 | 15
Exponential growth rate (r) Estimate from time series • data Fitting to incidence data • Logistic model with • negative binomial noise epigrowthfit package in R • Ma, J., Dushoff, J., Bolker, B.M. and Earn, D.J., 2014. Estimating initial epidemic growth rates. Bulletin of mathematical biology, 76(1), pp.245-260. mcmaster.ca June 26, 2020 | 16
Exponential Fitting Framework • Exponential growth rate (r) • Generation Interval mcmaster.ca June 26, 2020 | 17
Generation interval Time between • infections Focal individual • mcmaster.ca June 26, 2020 | 18
Generation interval Time between • infections Focal individual • Infection are hard to • observe Serial intervals • Time between • symptom onsets mcmaster.ca June 26, 2020 | 19
Exponential Fitting Framework • Exponential growth rate (r) • Generation Interval mcmaster.ca June 26, 2020 | 20
Exponential Fitting Framework • Exponential growth rate (r) • Generation Interval Euler-Lotka equation Wallinga, J. and Lipsitch, M., 2007. How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences, 274(1609), pp.599-604. mcmaster.ca June 26, 2020 | 21
Gamma approximation framework • Exponential growth rate (r) • Generation Interval (GI) • Mean GI ( ) • Dispersion ( ) Park, S.W., Champredon, D., Weitz, J.S. and Dushoff, J., 2019. A practical generation-interval-based approach to inferring the strength of epidemics from their speed. Epidemics, 27, pp.12-18. mcmaster.ca June 26, 2020 | 22
R 0 estimates Park, S.W., Bolker, B.M., Champredon, D., Earn, D.J., Li, M., Weitz, J.S., Grenfell, B.T. and Dushoff, J., 2020. Reconciling early-outbreak estimates of the basic reproductive number and its uncertainty: framework and applications to the novel coronavirus (SARS-CoV-2) outbreak. (In press) mcmaster.ca June 26, 2020 | 23
Parameter Uncertainties mcmaster.ca June 26, 2020 | 24
Parameter Uncertainties Uncertain of R 0 comes from these • parameters Important to propagate uncertainties • from all the parameters mcmaster.ca June 26, 2020 | 25
Forecasting Bayesian Discrete-time SIR • Dual beta-binomial process • Reports Transmission and • observation 2 week projection • Li, M., Dushoff, J. and Bolker, B.M., 2018. Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches. Statistical methods in medical research, 27(7), pp. 1956-1967. mcmaster.ca June 26, 2020 | 26
Summary • Easy to make a model • Extremely hard to make models that: • are informative • predict well • work in real time • Discrepancies between R 0 estimates is hard to understand • Method • Data • Hard to communicate clearly. • E.g. R 0 ~ 3 (2,4) mcmaster.ca June 26, 2020 | 27
Summary • Easy to make a model • Extremely hard to make models that: • are informative • predict well • work in real time • Discrepancies between R 0 estimates is hard to understand • Method • Data • Hard to communicate clearly. • Predictions of the short-term • E.g. R 0 ~ 3 (2,4) trajectories are useful mcmaster.ca June 26, 2020 | 28
Moving forward and preparing for the global pandemic • Interesting and important to figure out the discrepancies • What else? What do people want to know? mcmaster.ca June 26, 2020 | 29
Preparing for the global pandemic mcmaster.ca June 26, 2020 | 30
Preparing for the global pandemic mcmaster.ca June 26, 2020 | 31
Distributions of delays associated with Part 2 COVID-19 healthcare in Ontario, Canada mcmaster.ca June 26, 2020 | 32
Preparing for the global pandemic mcmaster.ca June 26, 2020 | 33
Distributions of delays associated with COVID-19 healthcare in Ontario, Canada mcmaster.ca June 26, 2020 | 34
Time intervals mcmaster.ca June 26, 2020 | 35
Time intervals ER time Isolation time Hospital admission time Specimen collection time ICU time Reporting time mcmaster.ca June 26, 2020 | 36
Chronological Episodes (Symptom onset) Delay Days mcmaster.ca June 26, 2020 | 37
Chronological Episodes (Isolation) Delay Days Duration Days mcmaster.ca June 26, 2020 | 38
Chronological Episodes (Specimen collection) Delay Days mcmaster.ca June 26, 2020 | 39
Chronological Episodes (ER) Delay Days Duration Days mcmaster.ca June 26, 2020 | 40
Chronological Episodes (Hospitalization) Delay Days Duration Days mcmaster.ca June 26, 2020 | 41
Chronological Episodes (ICU) Delay Days Duration Days mcmaster.ca June 26, 2020 | 42
Chronological Episodes (Death) Delay Days mcmaster.ca June 26, 2020 | 43
Chronological Episodes (Intubation) Delay Days Duration Days mcmaster.ca June 26, 2020 | 44
Chronological Episodes (Ventilator) Delay Days Duration Days mcmaster.ca June 26, 2020 | 45
Admissions, Durations and Occupancies Daily Admissions mcmaster.ca June 26, 2020 | 46
Admissions, Durations and Occupancies Daily Admissions Durations mcmaster.ca June 26, 2020 | 47
Admissions, Durations and Occupancies Daily Admissions Durations Occupancy mcmaster.ca June 26, 2020 | 48
Distributions of delays associated with COVID-19 healthcare in Ontario, Canada Changes over time mcmaster.ca June 26, 2020 | 49
New Confirmations Ontario, Canada mcmaster.ca June 26, 2020 | 50
Testing capacity mcmaster.ca June 26, 2020 | 51
Testing capacity mcmaster.ca June 26, 2020 | 52
Backlog ratio Backlog ratio Backlog (test) (test/day) newTests ~ X days to clear the backlogs mcmaster.ca June 26, 2020 | 53
Changes in Delays over time Backlog ratio mcmaster.ca June 26, 2020 | 54
Summary • Early detection is key in controlling the spread of covid • Reduce delay -> earlier isolation/treatment • What components we can take back to the modelling world to improve models • e.g. Hospitalization data • Duration spent in treatment • Combining different data streams to model mcmaster.ca June 26, 2020 | 55
McMaster Pandemic • SEIR model • Including Hospitalization time series • Using empirical delay/ duration distributions to parameterize the flow of the compartments Additional features • mobility from google and apple https://github.com/bbolker/McMasterPandemic mcmaster.ca June 26, 2020 | 56
Distributions of delays associated with COVID-19 healthcare in Ontario, Canada mcmaster.ca June 26, 2020 | 57
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