The trouble with your example is that each person within the community infects 1.2 others (0.8 in community + 0.4 in hospital); each person in hospital infects 0.9 others.

But your argument is sound. A more striking example: within a nodal group ( could be hospitals, could be supermarket staff) each infected person infects 5 others within that group, 5 in the general community; in that general community each person infects 0.01 in the nodal group, 0.08 in the general community - a really tight lockdown. Assume the nodal group is just 1% of the total community and initiate with 1 infected person in the nodal group, 99 in the general community. After 7 cycles you have 95000 infected in the nodal group, 96000 in the general community. Overall R rapidly converges to about 5.01 .

After 11 cycles the number of infected in the nodal group has reached the entire population of the UK - which is nonsense. What happens of course is that the nodal group develops herd immunity, and the infection dies away. This explains why a tight lockdown takes so long to show results. From that point, everything is OK, until another nodal group which has been suppressed under lockdown goes back to work!

CAPTCHA
This question is for testing whether you are a human visitor and to prevent automated spam submissions.