There's an interesting, if rather extreme, mathematical example dating from the 13th century which aptly demonstrates the power of the R0 (reproductive) factor. This involves grains of wheat placed on a chess board; 1 grain in the first square, 2 in the second, 4 in the third, 8 in the fourth, and so on. By the time you get to square 32 you need to be placing 2 billion grains, and by the time square 64 is loaded up the chess board would be holding more than 1,000 times the entire annual global production of wheat.

If, however, the multiplication factor is only 1.2 rather than 2 the final square only needs 97,000 grains.

If the R0 can be kept below 1, then numbers of new cases will decline but starting to decline still means they are going up. The balance between new cases and recovered then starts to plateau but it takes several weeks for any appreciable movement. Finally (we hope) the active cases start to fall and the Italian statistics show this happening (shaded in green), but the rate of decrease is excruciatingly slow compared with the earlier rate of increase.

[Because of the delays involved in testing and reporting, these figures are historic, so it's likely the real numbers of active cases started to fall a week or more beforehand. The numbers also only track hospital cases and don't necessarily reflect what's happening with less serious cases in the general population.]

So this is real knife-edge stuff, the decline is so small that the room for manoeuver by the authorities is limited. I can see only minor relaxation in May in Spain, Italy and the UK and this will be focused (I believe) on preventing the total collapse of our economies rather than personal freedoms.

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