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Carmen Lia Murall edited this page Apr 27, 2020 · 15 revisions

COVID-19 in Canada - data and epidemiological modelling

Early outbreak analysis: estimating epidemiological parameters.
This is for research and educational purposes only, not decision-making advice.
Ongoing work. Feedback welcome!

Carmen Lia Murall, PhD
contributors: Masih M. Saber PhD, Jonathan Dushoff PhD, Jessica Abbate PhD, Jesse Shapiro PhD
April 2020

1. State of the epidemic

April 4th, 2020

Nation-wide
image

According to the Public Health Agency of Canada (PHAC) the beginning of community spread was detected around the 28th of Feb [ref1]. Otherwise most of cases in the early part of the epidemic are due to travel importations of the virus.
The shaded region is when the numbers are less reliable (due to backlogs and lags of reporting).
The sudden jump in incidence cases is mostly due to Quebec's surge in numbers (see below).

Provincial (some examples) image

Quebec called a public health emergency, closing schools and businesses, a week after spring break (which was held the week of March 3rd, earlier than the rest of Canada). The return of spring breakers and the repatriation of snowbirds (Canadians living in warmer climates over the winter) lead to many importations while at the same time Quebec ramped up its testing capacity. Together, this lead to a surge in cases announced Mar 23rd.

image

Ontario was one of the first provinces to see cases. The rate of importations has begun to slow (after borders closed), implying most of the new cases we will see from now on are from local spread. Ontario is sharing individual-level data publicly [ref2], which includes if cases are travel-related.

April 14th, 2020
Cumulative cases
image

Incidence cases image

2. Estimating the effective reproductive number, Re

April 4th, 2020

Given that the federal and provincial governments implemented control measures early on in the epidemic, estimating R0 is really estimating the effective reproductive number, Re. There are various methods for doing this. One uses incidence data and the generation time (which is approximated with the serial interval instead). Using the package R0 in R [ref3, ref4] maximum likelihood, and a serial interval for COVID-19 [ref5], we get an overall Re for Canada (with data up to March 25th):
Re = 1.78 [1.67 - 1.89] code Here

For more on R0 and Re estimation, and how this was done for France, please see work by the ETE team from the CNRS Here

Here we plot the temporal variation of Re for Canada, Toronto and Montreal. Note that the last three to five days are not that reliable as there are lags in reporting.

image

In Montreal, after the surge of cases from the main importation events mid March, the R(t) will settle down to a more realistic value for SARS-COV2, which has been estimated below 3.

3. Estimating epidemiological parameters from model fitting

Early outbreak data can be fit by stochastic epidemiological models in order to estimate key parameters, e.g. R0. We modify an SEIR model to include pre-symptomatic and asymptomatic transmission, since both appear to be important to SARS-COV2 transmission. The schematic for this model is: image

A stochastic version of this model was used to infer parameters. We used maximum likelihood estimation and trajectory matching, while assuming the measurement error follows a Poisson distribution. Fitting and model trajectories were performed using pomp and deSolve packages in R [ref6].

image

The R0 in the figure is from the next-generation method [ref7] with the parameter estimates from the model fitting.

Also, the model estimates the R0's for each class, R0i = 2.2, R0a = 2.1, R0p = 1.8, and estimates around 50% of cases are asymptomatic, and the recovery rate of asymptomatics is around 2.7 days.

Note: model fitting and parameter estimation is work in progress, values will change.

Data sources

References

  1. PHAC COVID-19 epidemiology report https://www.canada.ca/content/dam/phac-aspc/documents/services/diseases/2019-novel-coronavirus-infection/en-surv-covid19-epi-update-2020-04-06.pdf
  2. ON website - data spreadsheets for download https://data.ontario.ca/dataset/confirmed-positive-cases-of-covid-19-in-ontario
  3. software package by Obadia, T., Haneef, R. & Boëlle, P. The R0 package: a toolbox link
  4. Obadia, Haneef and Boëlle (2012) The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks, BMC Medical Informatics and Decision Making, 12:147
  5. Serial interval data was taken from Nishiura et al. (2020) International Journal of Infectious Diseases.
  6. pomp: Statistical inference for partially-observed Markov processes, R package by AA King. https://kingaa.github.io/pomp/
  7. Heffernan et al. (2005) J R Soc Interface 2(4):281 and Diekmann et al. (2010) J R Soc Interface 7(47):873
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