Friday, April 3, 2020

Corona Virus Fears versus Facts

        Numerous experts in Universities ranging from Oxford and Cambridge in UK to Ivy Leagues in the USA are building Corona Virus scenarios based on statistical models. All these require parameters, which are based either on experience of other Epidemics/Pandemics, or the limited and imperfect data available on the SARS Corona Virus 2 (COVID).  As is to be expected, media ignores the complications and assumptions and presents a narrative based on the optimism/pessimism, fears/hopes and objectives of the commentator with respect to the country on which the comments are being made.
   In this note we examine the available cross country data on Corona Virus Cases and Deaths (as of 29th March, 2020) collected and organized by Johns Hopkins University to put the facts before the public and policy makers, so that they are not making decisions based on assumptions which can prove extremely costly to the country and its people. [i]
  We define the infection rate (IR) for the country as the ratio of Corona Virus Cases (CVC) to the population of the country (CVIR = 100*CVC/Population) and the Corona Virus Death rate (CVDR = 100*CVD/CVC). There are 128 countries for which this data is available. The summary statistics on the infection rate (CVCIR) is presented in Table 1. The average infection rate for the 128 countries, as of March 29, 2020 is 1/50th of 1%, with 53% o countries having an infection rate of less than 1/100th of 1% and 19% having an infection rate of 1/100th to 1/50th of 1%. 

Table 1: Summary Statistics for Infection Rate of Corona Virus
Note: Probability of any other country having such high infection rates is 0.3%
Source: Authors calculations based on Johns Hopkins Univ Data for March 29, 2020
     Only 13 countries have a infection rate of 0.06% or population with 4 of these countries at or more than three Standard deviations from the mean. These 4 countries are Italy, Spain, Switzerland, Iceland and Luxembourg. The last two have a population of 0.4 million and 0.6 million respectively.  Statistically this means that there is 0.3 per cent probability of any other country reaching above 0.16% .  It is also worth noting that the death for the three countries with highest infection rates are relatively low, with Iceland at 0.2%, Luxembourg 1.1% and Switzerland 2.0%. We consider Spain and Italy further below.
   Next let us look at the death rate for those identified by each country as infected by the Corona Virus. Table 2 summarizes this information. The average corona virus death rate(CVDR) is 2.2% of infected cases. 47 per cent of countries have a death rate of less than 1%, 18 per cent have death rate of 1% to 2.2%, i.e. 65 per cent of countries are below the mean. 22% of countries have death rate between 2.2% and 5% and 13% above 5%. Of the latter, Iraq, Spain and Indonesia are beyond two standard deviations from mean (probability ~68%) and Bangladesh, Italy and Guyana are beyond 3 standard deviations (probability ~ 0.3%). Bangladesh and Indonesia have an infection rate of less than 1/1000th of 1% of population and Guyana and Iraq have an infection rate of1/1000th of 1%. It’s quite likely that all four countries are only identifying serious cases in which the probability of Death is much higher. Spain (0.17%, 8.5%) and Italy (0.16%, 11%) are the two real outliers, with relatively higher infection and death rates than the rest of the World. Research on Italy shows that the death rate for people over 50 years of age with other medical conditions is much higher than for those under 50 years of age. For the latter the death rate is between 1% & 2% depending on whether they have other medical conditions or not.  It is clear that special precautions must be taken by, and for, people over 60 years of age.  

Table 2: Summary Statistics For Death Rate of Corona Virus 2
Note: Probability of any other country having death rates above 7.4% is 32%
Source: Authors calculations based on Johns Hopkins Univ Data for March 29, 2020
       In conclusion it’s possible to build scare scenarios from taking high infection rates and combining them with high death rates. For instance, if we arbitrarily combine the highest values of each, we obtain a death rate of 4 per 1000 of population. [ii]  The reality is quite different. The correlation coefficient between the infection rate and the death rate is only 0.12 a number close to nil, suggesting we are better off taking the mean values of both. This yields an expected death rate from SARS Corona Virus 2, of 0.46 per 1000 of population based on data available till end March,  2020.[iii]

[i] Surjit Bhalla and I have been working on the Corona Virus Data for the last two months, considering different hypothesis for the international and National spread of the Corona Virus and collecting data to test these hypotheses, formally. The research work is still in progress. The current blog uses this data and work done by both of us to produce a quick blog, bringing out some of the facts, without addressing every issue required in regular academic work.
[ii] This compares with a death rate of 7.2 per thousand in India (2017) and of 8.6 per thousand for the USA(2019).
 [iii] A linear projection of Indian cases to April 15, suggests that the number of Corona Virus Cases may rise to 26.078 and the number of Deaths to 678. The Expected Value, based on above data, for a country with 1.38 bi population is 287,350 cases and 6300 deaths.

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