[SystemSafety] NHS COVID-19 Contact Tracing App

[Peter Bernard Ladkin]

Peter,

On 2020-05-07 11:56 , Peter Bishop wrote:
> A contagion dies out when the replication factor R drops below 1, i.e.:
> 
> R = Ro [times] U < 1

R, or Rt or Re, is the effective reproduction number

> Ro is the "normal" number of people a person can infect.

R0 is the basic reproduction number, the average number of people infected by one person in a
situation in which all are susceptible.

> U is the proportion of the population that can still be infected

U is the proportion of susceptible people in the population

> The UK Covid figure for Ro was around 3 (before social distancing)

R0 has been estimated to be in the range 2.3 to 3.1 by a variety of studies from all over. If you
use the lower bound of 2.3, then 56% non-susceptible will do.

> So in a "do nothing" scenario
> 
> R <= 1, when U= 1/Ro= 1/3
> 
> i.e. when (1-U)=67% of the population  has been infected.

Not quite. When 67% of the population is not susceptible. You are assuming that having-been-infected
implies not-susceptible. There is debate on that, as well as for how long that situation lasts.

> If interventions (like distancing, testing, quarantine) can make Ro < 1, 

No, R0 is what it is. Nothing can "make" it different. You mean Re.

> the contagion will die out
> without infecting the whole population.

That's right, and indeed that is what happens.

This is known as the SIR model (there are others). A good explanation is
https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-introduction

Indeed, your observation generalises

R0 is obviously finite and positive. R0 times U > 1; so U > 1/R0 > 0. So there are always
susceptible people. In no case can *everyone* be infected (if infected implies non-susceptible).
Next question: what is wrong with this reasoning?

PBL

Prof. Peter Bernard Ladkin, Bielefeld, Germany
Styelfy Bleibgsnd
Tel+msg +49 (0)521 880 7319  www.rvs-bi.de





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