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Last updated: 2021-01-06-23:03 Melbourne time
Updates daily at 9:15 AM Melbourne time

The road to a COVID-free Victoria

Victoria has emerged from a fairly strict lockdown, that aimed for no local spread of the virus. This was successful - Victoria is now COVID-free and Australia as a whole has very low levels of the virus.

How have Victoria's restrictions affected the spread of the virus? The below plot shows how the effective reproduction number of the virus, R_eff has changed over time in Victoria, as well as how the daily cases have changed over time.

How on track was Victoria to meet its targets for easing restrictions in Melbourne? The below plot shows the 14-day average of daily cases, and the targets required to move to each step at their earliest possible dates. The requirement to move to the last step is zero cases for 14 days, which can't be shown on the plot.

Disclaimer

The projected trends are simple extrapolations of what will happen if R_eff remains at its current value. This does not take into account that things may change. As restrictions are lifted, the virus may have more opportunities to spread and so R_eff may increase. On the other hand as case numbers decrease and clusters are better tracked via contact tracing, R_eff may decrease. Finally, as case numbers get low, the random chance of how many people each infected person subsequently infects will become more important, and calculating a state-wide average of this (the definition of R_eff) will not be particularly meaningful or useful for prediction. As such the projections should be taken with a grain of salt—they are merely an indication of the trend as it is right now.

Methodology

2020-09-23 Data source change: These plots now use DHHS-provided historically corrected case numbers, backdated to the date the test was taken, instead of daily net case numbers. This means that reclassifications each day now modify historical data instead of simply subtracting from the case numbers on the date the reclassification was done.
2020-09-17 methodology change: The padding of the data is now based on a two-week fit instead of a one-week fit. This decreases the sensitivity of the latest estimate to day-to-day noise, instead keeping it more in line with longer-term trends. The uncertainty calculation has also changed—uncertainty in historical R_eff values was previously overestimated and is now calculated more accurately.
Daily case numbers have been smoothed with 4-day Gaussian smoothing:

N_smoothed(t) = N(t) ∗ (2πT_s²)^-1/2 exp(-t² / 2T_s²)

where T_s = 4 days and ∗ is the convolution operation.
Before smoothing, the daily case numbers are padded on the right with an extrapolation based on a exponential fit to the most recent fortnight of data.
R_eff is then calculated for each day as:

R_eff(t_i) = (N_smoothed(t_i) / N_smoothed(t_i-1))^T_g

where T_g = 5 days is the approximate generation time of the virus.
The uncertainty in R_eff has contributions from the uncertainty in the above-mentioned exponential fit, as well as Poisson uncertainty in daily case numbers, and an additional 20% uncertainty in daily case numbers - the latter is just a crude eyeballed figure of observed day-to-day fluctuations.
The extrapolation of daily case numbers is based on exponential growth/decay using the most recent value of R_eff and its uncertainty range:

N_extrap(t_i) = N_smoothed(t_today) R_eff(t_today) ^{(t_i - t_today)/T_g}

Source for case numbers: https://www.dhhs.vic.gov.au/victorian-coronavirus-covid-19-data and covidlive.com.au

Plot/analysis by Chris Billington. Contact: chrisjbillington [at] gmail [dot] com

Python script for producing the plot can be found at https://github.com/chrisjbillington/chrisjbillington.github.io/blob/master/victoria.py.