Why the ‘r’ Matters

by Les May

IN the context of discussions about the so called ‘r’ value; it is the number of people that one person suffering from Covid19 will infect on average.  In other words some sufferers will infect no one else, others will infect a number of people.  It can be calculated from the accumulated number of infections and how these accumulated numbers change with time, making it a value which applies to populations of potential sufferers.  It could be calculated by tracking of individual cases, but this is not usually done. The two methods may not yield the same value for ‘r’.  The population based method may produce a range of values. Numerically the difference between these values for ‘r’ may be small, 0.7 to 0.9 for Covid19, but the outcomes over say a two month period can be important.

In what follows I have assumed that the average time between someone becoming infected and being able to pass the disease on to others is six days. This is equivalent to ten generations of the virus in two months.

As can be seen from the above table, which has the starting point of 1000 infections and shows the number of new cases each week, the exact value of ‘r’ matters a great deal to the outcome after two months.  An ‘r’ value of 0.9 yields about two and a half times as many new infections as an ‘r’ value of 0.7. An ‘r’ value of 0.5 leads to the virus having no one to infect and dying out within two months.  The actual values for the number of new infections would differ from the calculated values due to the fact that they do not take into account the differing numbers of people a single Covid19 sufferer might themselves infect. This will also mean that when the number of new cases is very low none of them may go on to infect others so the number of new cases would fall abruptly to zero.

For comparison purposes the number of new confirmed cases was reported as 1653 on 2 June 2020.  The total number of cases, confirmed and unconfirmed is estimated to be five times higher.   If correct that would translate into about 18,000 new cases in the next two months if ‘r’ is 0.7 and about 50,000 new cases if the ‘r’ is 0.9 unless ‘test, track and trace’ leads to a considerable decline in ‘r’.

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