I am very dubious about the Manchester paper that is just analytical equations and theoretical modelling,
vs
Spain, based on a study from their Ministry of health checking for antibodies in 60,000 blood tests
when the results give 19 million Brits have been infected, over 25% of the population 
vs
Spain, where their Ministry of Health estimates only 5% of the population, 2.3 million people 
- and Spain has a slightly higher death / million than the UK
I did maths modelling for nearly 40 years and we would normally trust actual tests over theory