Coronavirus Projections
Updated (04/06/20 3:19 EST)
Background
There are many models that are being used to predict the outcome of the Coronavirus outbreak. This article is my documentation of my efforts to develop such a model. The basis for this model is described in "Determination of the Uncertainties in S-curve Logistic Fits" (see Source 1). It is an adaption of the efforts currently being done by Theodore Modis (https://www.dhirubhai.net/in/theodore-modis-140222/).
MATLAB Code: https://github.com/HookAsnooK/Coronavirus
Assumptions and Concerns:
- The error used to interpolate from the "confidence tables" is the average of the error between the data and the nominal S-curve. As a result, the error is heavily dependent on which data is chosen to be included in the projection. I have used personal judgement in defining when to start the projection model in time.
- This model is believed to be accurate if the data is no longer exponentially increasing and the time a which the distribution has peaked (t0) has been reached.
- This model assumes that the data being reported is valid and does not consider scenarios such that the number of cases is being under reported, etc.
- This model does not consider the impact of extraordinary events such as country-wide efforts to prevent spread, etc.
Results
US Disclaimer: I scaled the error by 10 in order to get the confidence interval. The reason I am ok with this is because I think the micro trend has been subject to the individual city-wide spreads, causing a high amount of error in the macro trend. Another possible reason is that my math is off somewhere.
<Placeholder: Iran, Spain, France>
Conclusions
The s-curve projection approach aligns well with the data that has been collected in China and South Korea. For the projections in Italy and the United States, it is still too early to have an accurate projection due to the exponential behavior in the growth of cases.
(3/18/20) Current US project at +90% confidence is 511,000 people will contract the virus. Given the currently population of the US is 317M, this would suggest that 0.16% of the population will contract the virus. I believe over the next week as cases continue to emerge and testing capability improves, this number will grow dramatically and the projection will become more refined.
(4/6/20) For the US, I am optimistic that with the slowing rate of Coronavirus cases and the seriousness that the general population has taken in their social distancing efforts, we will continue to see a decline in the rate of Coronavirus case. However, I also believe that if society were to waiver in their efforts, we may need additional outbreaks in Tier 2 cities that could result in the trend continuing for some time.
Sources
Revision History
- Updated (03/18/20 12:42 EST) - Original draft
- Updated (03/19/20 8:57 EST) - Updated US and Italy graphs
- Updated (03/19/20 8:57 EST) - Updated US, removed confidence bands until we exit the exponential phase
- Updated (04/06/20 3:25 EST) - Updated US and conclusions
Professor of Chemical Engineering, Director APT Lab, co-founder SyNest PC, Chief Scientific Advisor CHORUS Cluster, specialist in Emission Control/Nanoparticle Technologies/Solar Fuels/Sustainability through Circularity
4 年The US data are shown below for the initial period plotted in semi-log coordinates (left image). The data demonstrate an initial s-curve with a ceiling at 15 which when fitted and projected backwards generates an additional 10 missed incidents that have occurred since Dec 21 (right image). This implies that in the US the virus was transmitted during the Christmas holiday season filling a niche of 25 diagnosed cases and then following an inception period it took off starting a second logistic which currently is still in its exponential phase. We still have a long way to go.
Professor of Chemical Engineering, Director APT Lab, co-founder SyNest PC, Chief Scientific Advisor CHORUS Cluster, specialist in Emission Control/Nanoparticle Technologies/Solar Fuels/Sustainability through Circularity
4 年OK Wayne Moss I am collecting here previous comment under posts to have them in one place. USA. Data taken into account until March 19, 2020, total no of infected individuals. No reliable estimates for a logistic growth curve can be made without evoking additional constraints. Using a constraint on the life cycle (t_90 - t_10)? we can obtain the? curve, shown in the first image consistent with the data.? What is the meaning of this? If measures are taken to impose a life cycle of ~14 days we can expect the ceiling to be at the indicated figure with associated confidence levels. Of course this does not mean that things will evolve in this way. The only such example currently is South Korea and China (life cycles of 12 and 16 days respectively). As it is too early to tell the effectiveness of the measures in the US we can make numerous projections with their associate confidence levels (e.g. your US graph above). Looking closer to the US data we can see some interesting initial phase where a partial s-curve exists and by projection back in time we recover early data that were missed (CONTINUED IN THE NEXT COMMENT)
Quantitative Research Director at TD Securities Automated Trading
4 年I have not followed the development of the policies in the US too closely so correct me if I am wrong but shouldn't we need the full lockdowns enabled to expect the breakdown of the exponential into a sigma curve? I feel like the moment the exponential breakdowns strongly depends on the moment the governments enact these policies (lockdowns + intense testing policy) as we have seen in China and SK, and expect to see the effects in Italy shortly.? I understand here it's not really the goal to include the policies of the different countries but perhaps this specific event can be parametrized into this t0.? Also, perhaps it could be interesting to normalize the number of cases with respect to the country total population.?
The + and - confidence intervals cross for US? I don’t think it’s prudent or useful to fit a logistic curve for the US data yet. I’ve been watching the daily growth rate (Cases_Today/Cases_Yesterday) which is a good indicator of if the spread is accelerating or slowing. It’s around 1.32 and fairly stable currently. Therefore can’t determine the inflection point in the S logistic curve. What we see over the next couple weeks will be interesting. People in the US are finally taking it seriously , but we could easily see an apparent increase as testing becomes more widespread. I hope people don’t use this to say “social distancing doesn’t work”.