Natura capta ferum hominem cepit : coronavirus epidemies, Part II

Coronavirus epidemies, COVID-19 (2020) e SARS (2003). Part II: Covid-19, since April 26

(Nature, vanquished, took the fierce man captive)

Enrico Canuto, Politecnico di Torino, Docente a riposo, Former faculty

Since April 26

April 26

I start again studying Covid 19 data, by focusing on Japan data from WHO. I do not know whether they refer to positive (confirmed) cases irrespective of symptoms or just to symptomatic people. Dates correspond to WHO data retrieval, which implies at least one day of delay (you must subtract 1).

Japan. As shown in Figure 1, Japan outbreak can be divided into two phases: (1) in the first phase ending  at about day 91 (March 31) the infection rate progressively diminished to a very small value, corresponding to a long time constant (up to 35 days), until March 31, (2) when, abruptly, the time constant dropped to be less than 10 days, implying a much faster infection rate. The second phase ended around day 110, when likely the peak daily rate was reached.  Current Japan data seem to indicate the third phase, when the daily rate is diminishing. What occurred in the days before March 31?

On 27 February (day 58) prime minister S. Abe requested the closure of  schools from March 2 (day 62)  until early April (end of spring vacations). Before this date quarantine only concerned people from abroad. On March 22 (day 82) thousands of people attended two public events.  On April 7 and 16 (days  98 and 107), S. Abe proclaimed the state of emergency in all the prefectures, but no lock-down policy was imposed. On April 10, some business activities were requested to stay close. Major festivals were either cancelled or postponed.

Figure 1 - Japan. Left: exponential fit time constant, data RMS and error/data relative RMS. Also data RMS prove rate change. Right: mid term (until day 90) and long term fit, including weekly oscillations. They fit mid-term data, but not long-term data where phase changes.

The complete raw data, estimated and extrapolated profiles are shown in Figure 2. Again, the weekly correction has been added. Data fitting seems suggesting that the peak rate has been surpassed, but of course … caution.

Figure 2 - Japan. Daily rate of positive cases, April 26.
May 4 – Sticky Italy

Italy. Quarantine phase 2 starts today, as part of industrial activities reopen and people mobility is less constrained. It is of interest to observe infected and hospitalized status and make some prediction. Figure 3, left, shows raw data and extrapolation of actually positive and hospitalized cases. Both look slowly decreasing. In Part I we assumed, by comparison with China profiles, that a time discriminating between quarantine period and mobility recovery may be the negative peak time of the hospitalized daily rate. Figure 3, center, shows two negative peaks, the earlier equal to 112 day (April 21) refers to hospitalized people and the later equal to 132 day (May 11) to positive cases. This would imply that Phase 2 should have started later than May 4, account taken of the current high volume of positive cases.

We should remark that only recovered and died people have been removed from total positive cases, since home quarantined people have not been, up to now diagnosed as uninfected. Thus the positive profiles in Figure 3 have to be taken as upper bounds of the real situation, which may justify May 4 as the starting date of the second phase. A confirmation comes from the decreasing fraction of tested positive in Figure 3, right.

Figure 3- Italy: positive and hospitalized cases. Left: cumulative profiles. Center: daily rates. Right: fraction of positive tested cases.

The above data and extrapolations have been used to estimate initial and current reproduction factors  R0 and  R(t) as well as initial and current affectable people s0 and s(t) in both cases.