Reproduction Ratio (RO)

Introduction

a measure of contagiousness
RO = the number of secondary infections each infected individual produces
this will vary with:
- the method by which it is estimated
- The rate of contact between individuals in the host population
  - eg. social distancing will reduce R0 if it is droplet spread
- The probability of the infection being transmitted during contact:
  - ease of transmission
  - level of PPE
  - viral factors
- The duration of infectiousness
essentially for an epidemic to disappear whilst there are still susceptible population, the R value generally needs to be less than 1 until the epidemic resolves and the pathogen is eliminated

If R0 is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.
EACH method of estimating it is likely to give different values of RO as they each make different assumptions and have their own errors.

R = R0 x proportion of population susceptible
the disease spreads to all the community if it has an R0>1
R0 needs to be less than 1 to contain an epidemic and modelling suggests the community need to be at least 80% compliant with strict social distancing rules ¹⁾
the lower the R0 is, the flatter the growth curve of infection and the lower the impact on the healthcare system and overall mortality and morbidity, although it will tend to prolong the epidemic

essentially uses statistical methods to analyze distances between cases and usually requires analysis of contact tracing data.

During the initial phase of an epidemic, the number of secondary cases increases exponentially, with each infection producing R 0 new infections per generation assuming a constant doubling time (td)
R0 = 1+(infectious period/doubling time)*ln2

estimate the transmission rate, β, from epidemic data using a linear regression model
eg. regression model can be defined as log (−log (1−E(C) / S)) = log (β) + log (IΔt / N)
- where C, S, I are respectively the number of newly-infected, susceptible, and infectious at the start of the time interval Δt.
R0 = β x infectious period

uses trial and error iterations to find the best fit curve for the actual data using SIR equations

as number new cases = βSI / N
thus if one knows the new cases each day, the total population (N), the number of susceptible population (S) and the number infectious (I) then one can calculate β and then if you know the infectious period you can calculate RO via:
- R0 = β x infectious period

Herd Immunity Threshold (proportion of population needed to be immune to prevent an epidemic) = 1 - (1/RO)

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