# 1 Introduction

This paper contains estimates for the effective reproduction number $$R_{t,m}$$ over time $$t$$ in various provinces (and health regions) $$m$$ of Canada. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was f375c64277b7e5fd535c882031ceca88dc14db31.

• On 29 May 2021 all plots and maps were updated to consistently not plot reproduction number estimates where the 95% confidence interval associated with that estimate is wider than 1.

# 3 Data

Data is downloaded from the Git repository associated with [3]. This contains the daily cases and deaths reported for Canada by province and health regions.

Repatriated cases are removed and provinces as found in [4] are grouped per the table below:

Province Groupings
Province Province Grouping
Alberta Alberta
British Columbia British Columbia
Manitoba Manitoba
New Brunswick Maritime Provinces
Nova Scotia Maritime Provinces
Nunavut Territories
Northwest Territories Territories
Ontario Ontario
Prince Edward Island Maritime Provinces
Quebec Quebec
Yukon Territories

The only adjustments to the data relates to large numbers of deaths reported in Ontario on 2 and 3 October 2020 “due to a data review”. 111 of the deaths reported on these two dates are deaths that occurred during the prior spring and summer (see [5] and [6]). Based on this these deaths were removed from 2 and 3 October and added back in prior days in proportion to deaths reported up un till 30 September 2020. The net effect is no change in reported deaths, but a peak in October is avoided which would have biased estimates.

# 4 Methodology

The methodology is described in detail here.

# 5 Results

## 5.1 Cases

Below a 7-day moving average daily case count is plotted by province on a log scale:

## 5.2 Deaths

Below a 14-day moving average of daily reported deaths by province is plotted on a log scale.

## 5.3 Current reproduction number estimates by Province

Below current (last weekly) reproduction number estimates are tabulated.

Estimated Effective Reproduction Number by Province
province Estimated Type Daily Count (Last Week) Week Ending Reproduction Number [95% Confidence Interval]
Alberta cases 17 2022-12-11 0.13 [0.11 - 0.17]
Alberta deaths 7 2022-12-11 1.05 [0.77 - 1.38]
British Columbia cases 0 2022-12-11 0.00 [0.00 - 0.01]
British Columbia deaths 0 2022-12-11 0.03 [0.00 - 0.11]
Manitoba cases 0 2022-12-11 0.00 [0.00 - 0.01]
Manitoba deaths 0 2022-12-11 0.98 [0.02 - 4.84]
Maritime Provinces cases 22 2022-12-11 0.13 [0.11 - 0.15]
Maritime Provinces deaths 2 2022-12-11 0.65 [0.36 - 1.02]
Territories cases 0 2022-12-11 5.00 [0.12 - 18.38]
Territories deaths 0 2022-12-11 5.06 [0.13 - 18.64]
Ontario cases 0 2022-12-11 0.00 [0.00 - 0.00]
Ontario deaths 0 2022-12-11 0.03 [0.00 - 0.10]
Quebec cases 465 2022-12-11 0.48 [0.44 - 0.52]
Quebec deaths 2 2022-12-11 0.41 [0.23 - 0.64]
Saskatchewan cases 0 2022-12-11 0.00 [0.00 - 0.01]
Saskatchewan deaths 0 2022-12-11 0.05 [0.00 - 0.19]
Canada cases 504 2022-12-11 0.31 [0.28 - 0.35]
Canada deaths 11 2022-12-11 0.38 [0.30 - 0.48]

## 5.4 Estimated Effective Reproduction Number for Canada over Time

Below we plot results for Canada as a whole.

## 5.5 Estimated Effective Reproduction Number for Provinces over Time

Below we plot results for each province.

## 5.6 Detailed Results

Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.

# 6 Discussion

Limitation of this method to estimate reproduction number are noted in [1]

• It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
• It relies on an assumed generation interval assumptions.
• The size of the time window can affect the volatility of results.
• Results are time lagged with regards to true infection, more so in the case of the use of deaths.
• It’s sensitive to changes in case (or death) detection.
• The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

# 7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

# References

[1]
A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133.
[2]
A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013.
[3]
I. Berry et al., “A sub-national real-time epidemiological and vaccination database for the COVID-19 pandemic in Canada,” Scientific Data, vol. 8, no. 1, p. 173, Dec. 2021, doi: 10.1038/s41597-021-00955-2.
[4]
I. Berry, J.-P. R. Soucy, A. Tuite, and D. Fisman, “Open access epidemiologic data and an interactive dashboard to monitor the COVID-19 outbreak in Canada,” Canadian Medical Association Journal, vol. 192, no. 15, pp. E420–E420, Apr. 2020, doi: 10.1503/cmaj.75262.
[5]
G. Rodrigues, “Ontario reports new record of 732 coronavirus cases, adds 76 more deaths due to data cleanup,” Global News. https://globalnews.ca/news/7373691/ontario-coronavirus-cases-october-2-covid19/, October 2, 2020 9:36 am.
[6]
R. Rocca, “Ontario reports 653 coronavirus cases after record number of tests completed,” Global News. https://globalnews.ca/news/7376209/ontario-coronavirus-cases-oct-3-covid19/, October 3, 2020 9:31 am.