சுருக்கம்

Total confirmed cases (blue), total deaths (red), and reported deaths on the last ten days (dotted black).

This chart has been made using the WHO daily reports (see https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/). Though countries are committed to report to WHO every day, some country reports are missing, leading to "steps" in the curve. This is caused by messy report and can't really be corrected. Please note that due to time zones and time of report, the figure for a given day according to WHO may not be that of official sources.

The growth of a pandemic in its initial stage is exponential, meaning that the percentage of increase from one day to another is (roughly) constant. This, in turn, means that in a semi-logarithmic plot, the slope is (roughly) constant, therefore the curve is (roughly) a straight segment. In the end of a pandemic, no additional victims are reported, and the curve is a flat horizontal. In between, the public health policy is to bend the curve down. A change in the policy or its efficiency leads to a change in the slope.

To describe the pandemic's evolution, a daily report of victims or deaths is not really informative in the aftermath. The relevant description is, where are the slope changes, which indicate a change in the pandemic's regime? Those inflection points are the limits within which the description of what has occurred can be homogeneous. Most countries start with very weakly sloped curve, almost horizontal, with few SARS-CoV-2-positive patients : that is the contained stage. Then the curve rises all of a sudden, this is the local starting point of the pandemic, the virus has escaped in the wild and is not contained in the hospital any more. Some weeks later the semilog curve has a first inflection point, this is the effect of measures taken at the end of the "wild" phase, which slows the growth regime. There may be some more regime changes before the curve bends downwards towards very low values, which is more or less the (local) end of the pandemic.

Those intervals, where the curve is (roughly) a straight segment, are best seen when they are illustrated by a reference thin straight line. This "best fit" line is a standard statistical function of the data; and if the segment is straight enough, the choice of starting and ending point for the segment makes little difference. Even when the curve does slope downwards and no straight segment can be identified, a straight reference line that underlines the tangent at a point is useful in judging the curvature itself, though the tangent point is of course arbitrary in that case.

Please do not use these "best fit" lines for extrapolation : the mathematics of epidemics involves many different effects and the modelling needs to take into account many different uncertainties. Whatever the slope of the curve is at a given time, it will eventually curve down (switch to a horizontal). In the case of the COVID-19 pandemic, the values may increase again with repeated peaks over the 12-18 months until vaccines are judged to be safe and are mass-produced and provided to the world's population.

அனுமதி

இந்த ஆக்கத்தின் காப்புரிமையாளரான நான் இதனைப் பின்வரும் உரிமத்தின் கீழ் வெளியிடுகின்றேன்:

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நீங்கள் சுதந்திரமாக:

• பகிர்ந்து கொள்ள – வேலையை நகலெடுக்க, விநியோகிக்க மற்றும் அனுப்ப
• மீண்டும் கலக்க – வேலைக்கு பழகிக்கொள்ள.

கீழ்க்காணும் விதிகளுக்கு ஏற்ப,

• பண்புக்கூறுகள் – நீங்கள் பொருத்தமான உரிமையை வழங்க வேண்டும், உரிமத்திற்கான இணைப்பை வழங்க வேண்டும் மற்றும் மாற்றங்கள் செய்யப்பட்டிருந்தால் குறிப்பிட வேண்டும். நீங்கள் ஏற்புடைய எந்த முறையிலும் அவ்வாறு செய்யலாம், ஆனால் எந்த வகையிலும் உரிமதாரர் உங்களை அல்லது உங்கள் பயன்பாட்டிற்கு ஒப்புதல் அளிக்கும் படி பரிந்துரைக்க கூடாது.
• அதே மாதிரி பகிர் – நீங்கள் ரீமிக்ஸ் செய்தாலோ, உருமாற்றம் செய்தாலோ அல்லது பொருளை உருவாக்கினாலோ, உங்கள் பங்களிப்புகளை அல்லது இணக்கமான உரிமம் கீழ் அசலாக விநியோகிக்க வேண்டும்.

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