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Fighting Covid-2019: The Great Turn comes

Part 1. How many people will kill the coronavirus?


Since the writing of my first article on forecasting the coronavirus epidemic, a little over a week has passed, but much has changed.

First of all, there was a turning point in the dynamics of the global epidemic: the curve of new deaths reached its peak. This means that the first period of the global epidemic is over, when every day the number of new deaths grew almost exponentially.

A week ago, I would gladly say that now the epidemic will also quickly decline. But the new data accumulated over the past week have dispelled this optimism. Indeed, in some countries (such as China, and possibly Germany), the development of the epidemic is described by a logistic curve. But other countries disappointed me.

Fresh forecast of the number of victims of the epidemic and beautiful pictures under the cut.

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It turns out that the sloppiness of the population, which is in no hurry to implement quarantine measures established by the government, as well as the indecision of the governments of some countries to introduce such measures, lead to the distortion of the logistic curve.

At first, indeed, the epidemic is gaining momentum, and every day the number of deaths increases. Then it reaches a maximum. And after that ... sticks at that maximum. This is how it happened in Iran and Italy.





If we were dealing with a logistic curve, immediately after the maximum there would have been a decline. Moreover, if we consider the first derivative of the logistic curve (daily mortality curve), then it is symmetric about the point of its inflection. This means that the sharpness of the left side of the peak of the curve would be equal to the sharpness of the curve at the start point of the rise, as shown in the figure below.

Unfortunately, in many countries this is not so. The top of the curve is flat, and it is completely different from the sharp start of the curve. Depending on how long the population quarantines, the length of the flat portion of the daily mortality curve increases.

If you look at the curve of total mortality, then it no longer looks like a logistic one. It was as if a logistic curve was cut in half and a straight line inclined with respect to the horizon was inserted between its halves. In this area, the daily number of deaths increases by approximately the same amount. Look again at the case of Iran and Italy.





And here is the daily mortality curve around the world. She only went to her maximum. Unfortunately, it is not easy to predict how long the curve will stay in the region of its maximum before the decline in the number of deaths begins. However, based on general considerations, one must think that due to the large number of countries with a population profiling quarantine measures, the top of the global pandemic schedule will also be flat.





In the last article, we mentioned the choice before us: to develop a procedure that would not only give the most probable forecast of the number of deaths, but also predict the error. That is, we need to have an optimistic forecast for the dead (such that the final number of dead would be greater than this forecast), as well as a pessimistic forecast (which would exceed the final number of dead).

Over the past week, we faced yet another task: to describe the dynamics of mortality taking into account the flat top effect, when it is no longer possible to use the classical logistic curve for forecasting.

The author was able to successfully solve both problems, and to develop a forecasting technique that would allow one to calculate the forecast error, and also take into account the flat top effect.

Unfortunately, at present the author does not have enough time for the author to fully describe the constructed forecasting model. Therefore, in the first part we will present the promised forecast for the world as a whole and for some countries separately, and in the next parts of this article I will describe how these forecasts were received and how readers can repeat the forecasting in Python.

Here is the promised forecast. I plan to update it at least once a week, using new data. But I will keep the previous forecasts in order to illustrate the dynamics of modeling.



By the way, they asked me why I did not use Excel for forecasting? I answer: Excel has built-in mechanisms that allow you to find parameters that correspond to the minimum of an arbitrary function. Although 99% of users, these mechanisms are not known, and their use is not entirely trivial. This is the level achieved in the previous article.

But in the following parts of this article we will conduct simulation modeling, when for each of the countries we will perform a similar procedure several thousand times, in a certain way changing the incoming set of statistical data. T.N. bootstrap simulation.

The author has no idea how to do such a simulation in Excel without using VisualBasic. At the same time, in Python, the transition from searching for a minimum of a function in a single case to searching in several thousand cases is carried out by writing several lines of code. I will show this trick in the third part of this article.

Soon there will be a link to part 2 of this article.

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