Intra-Country Spread of Corona Virus: Wo Index

Joint Blog with Dr. Surjit Bhalla, also  available at, https://medium.com/@tranquil_keppel_sheep_341/a-new-blog-time-will-tell-54e4b35a0557?sk=f3246146a6691194d33a2c8ca7d67369 .

          We develop and use an Index Wo related to the R0 index used by epidemiologists to judge the progress made in controlling the spread of the Corona Virus within countries. The critical value of the Index is one. A value greater than one suggests that the Viral transmission is in its expansionary phase. A value lower than one indicates that the spread of the virus is slowing and is headed towards zero. There can and have been situations in which the virus went into a recessionary phase, but recovered and expanded in a second phase, before returning to the recessionary phase.

   First, we examine the progress made in the four large democratic countries India, USA, Japan, and UK. Table 1 summarizes the Wo trends in India, USA, Japan, and UK, in terms of the latest value of the index for each country and the average of the index for the past one, two, three and four weeks. This puts the current index into perspective, so we can judge whether the current value is part of a trend, or merely a spike or temporary occurrence. All four countries have gone below one, the critical threshold of transmission. The USA with an index of 0.4 and UK with an index of 0.5 have made greater progress in slowing transmission of the Corona Virus than Japan (0.8) and India (0.9). With the index averaging less than 1 for the last two weeks and a clear down trend over the last four weeks, both USA and UK seem to be on the slow road to recovery. Japan has a more checkered history, with initial success followed with a reversal, with index averaging 1.06 during the 7 days ending April 17, 2020.   India has just crossed the critical threshold from the expansionary to recessionary phase of the Corona Virus. Though the trend is clearly down in India, it is important to ensure that the trend is not reversed in the second half of April.

Table 1: Index (W0) of Speed of Spread of Coronavirus Cases within Country

          (based on Corona Virus cases up to 17 April 2020 

 Figure 1 shows the evolution of the index (Wo) since the start of the epidemic in each country, with Japan on the right-hand scale and others on the left-hand scale. Note that the higher values of the Index Wo are merely a statistical artifact as cases rise from 1 to 2 etc.

Japan shows the cleanest pattern, rising continuously from the 22^nd day to a peak of 40 on the 29^th day and then falling continuously thereafter to 1 by the 40^th day. The index spiked to above 1 on April 6^th, stayed above 1 till April 16^th; since then it has been on a steady declining trend and preliminary data for April 21^st shows the index to be below 0.5. Barring a big surprise, it is now apparent that there is little prospect of a second wave in japan, as some are speculating. But Time Will Tell!

India: Wo rose to a peak of 12 on the 32^nd day, while showing secondary peaks both on the way up and on the way down. In the latter case the secondary peak of 3.2 occurred on day 47 and 49^th day of the pandemic. Since then it has declined gradually to 1 on day 71 of the pandemic.

UK: Wo rose to a peak of 13.6 on the 34^th day, while showing secondary peaks both on the way up and on the way down. In the declining phase the secondary peak of 5.7 occurred on day 45 of the pandemic in UK. Thereafter Wo has declined to 1 by the 61^nd day of the pandemic in UK.

USA: Wo shows a slightly different pattern with several subsidiary peaks before reaching the final peak of 9.7 on day 57 after which the Index has declined gradually and continuously to reach 1 by day 71 and  0.5 on day 78 of the pandemic.

The order of peaking was therefore Japan, India, UK and then USA. The order of reaching the threshold value of 1, separating the accelerating phase from the deceleration phase of the pandemic, was Japan, UK, and USA & India (figure 1). Japan reached this value 10 days before the UK.

What do we learn from the Wo pattern for different countries?

·         First, that to a surprising degree, the pattern is remarkably similar. Note that the first major peak in three countries (India, Japan, and the UK) occurs within days of each other [the days are counted as days from the first episode of the crisis). In the US, the peak-peak occurs about three weeks later.

·         Second, the recessionary phase, once it sets in, is fast in all the four countries.  

Figure 1: Speed of Transmission of Corona Virus and Critical Threshold: Index Wo