I think this twitter thread is a good explanation of the effects of a more transmissible strain:
twitter.com/AdamJKucharski/status/1343567425107881986
The illustration from Adam Kucharski's (an epidemiologist at the Londons School of Hygiene and Tropical Medicine) thread:
As an example, suppose current R=1.1, infection fatality risk is 0.8%, generation time is 6 days, and 10k people infected (plausible for many European cities recently). So we'd expect 10000 x 1.15 x 0.8% = 129 eventual new fatalities after a month of spread.^
What happens if fatality risk increases by 50%? By above, we'd expect 10000 x 1.15 x (0.8% x 1.5) = 193 new fatalities.^
Now suppose transmissibility increases by 50%. By above, we'd expect 10000 x (1.1 x 1.5)5 x 0.8% = 978 eventual new fatalities after a month of spread.^
That doesn't take into account any further preventable deaths because people can't get the treatment for COVID-19 they need because the hospitals can't cope nor deaths from other diseases because the hospitals are full of patients with COVID-19.