• Stephen Grice

Improvements to the SIR+B mathematical methods

Updated: Jul 23, 2020

In this blog post we provide details into an update our SIR+B method. The method now includes some improvements in Error and noise Handling and forecasting. The updated report for the SIR+B method is here.

In summary we have improved the SIR+B method based on feedback in the following ways.

Error and noise handling

We have updated how we handle errors and noise that result from real world data of COVID-19 positive daily case data. Previously we have used standard Newton-Coates smoothing functions. These smoothing functions reduce local noise to greater or lesser degrees depending on the order of method chosen. We have replaced this approach by applied Discrete Cosine Transform (DCT) to the COVID-19 positive daily case data. This method allows us to remove noise by filtering out frequencies that are not epidemiologically justified. Transforming the DCT from frequency domain back into the time domain allows us to reduce noise, not just locally, but across the entire region of the epidemic. This has a significant calming effect on the calculation of Reff and it has significant benefits.

The reduction in noise that was achieved by applying DCT has improved stability and narrowed the confidence intervals of our calculations.


The SIR+B forecast intervals have increased in certainty from reduction in noise. Forecasting COVID-19 is extremely hard but also important. By now enough global data and experience has accumulated showing the various effects such as social distance policy on disease propagation and the effects of outbreaks in South Korea and Victoria, Australia. Reff is more responsive to social distance policy – both official and unofficial – than to any other factor. But humans are unpredictable by nature. Our methods now project forwards based on the recent past (6 weeks) and are more certain than before. Like any prediction it can be proven incorrect in hindsight if the recent past behavior is not a good prediction of immediate future behavior. This happens in times of discontinuities which we can expect more in countries which have significant and growing problems like the United States. We now trust our forecasts more than others because we believe the responsiveness of our method, combined with the improvements mean that our method has all the desirable features of noise reduction and accuracy and none of the undesirable features of the statistical approaches of other methods. The computed results are empirically more accurate and justified, and on a firmer theoretical basis than other methods we have seen.

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