1/n An explainer from @edyong209 on R0, the basic reproduction number (or ratio), an important quantity in infectious-disease epidemiology. He does a good job of deflating the hype around the specific estimates of R0 for the current #nCoV2019 outbreak.
2/n A key point, which he doesn't emphasize, is that R0 applies *at the start of an epidemic*. The zero ("naught") refers to the generation of the epidemic. The zeroth generation is right at the start.
3/n Why? Epidemics are nonlinear. The number of new cases is generally proportional to the product of the number of infectious cases and the number of susceptible people. As people become infected, this product increases then declines. 
4/n R0 is the *average* ratio of the number of cases in generation 1 to generation 0, i.e., on average, how many people are infected by the first (index) generation? If it's greater than 1, an epidemic is likely.
5/n Obviously, there are ratios of cases between subsequent generations too. We often call these the effective reproductive numbers Ri ("R-sub-i"), where i stands for the index of the generation (0,1,2,3,...,n).
6/n If we can bring Ri down below 1 -- and keep it there -- we control the epidemic. If the population is well-mixed, we need to cure, vaccinate, or quarantine a fraction 1-1/Ri of the population to do this.
7/n So if Ri=2.5, we need to vaccinate (say) 1-1/2.5=0.6 of the population. For Ri=3.5, it's 0.71. if Ri=1.5, it's only 0.33. So the higher Ri (including R0) is, the harder it is to control.
8/n As @marcelsalathe and others have shown, if the population is not well-mixed, the fraction you need to vaccinate can be much higher (doi.org/10.1098/rsif.2…)
9/n The other thing that @edyong209 highlights nicely is that R0 is not simply a property of the pathogen. It depends fundamentally on the social system of the host.
10/n For the simplest model of an epidemic, R0 is simply the product of the transmissibility of the pathogen, the duration of infectiousness, and the average rate of contact between susceptible and infectious hosts.
11/n This last thing can vary a lot depending on pop densities, norms of social interaction, public health interventions, etc. So for the same pathogen, R0 will be different in different places, times, contexts, etc.
12/n It also means we can control epidemics. Public health works! Social distancing can help reduce the reproduction ratio of an infection, even in the absence of an effective vaccine.
13/n For calculation of R0, I'm with @Caroline_OF_B: keep it simple. An approximation that's as good as any other when you don't know much is
R0 = 1 + (rate of increase of infections) x serial interval
The serial interval is the average time between cases
R0 = 1 + (rate of increase of infections) x serial interval
The serial interval is the average time between cases
14/n As with SARS, the serial interval for #nCoV2019 seems to be about 7-10 days (e.g., doi.org/10.1016/S0140-…)
15/n The rate of increase of infections (early in the epidemic) is:
r = ln(Nt)/t
where Nt is the number of cases at time t and t is the time since the emergence of the outbreak.
r = ln(Nt)/t
where Nt is the number of cases at time t and t is the time since the emergence of the outbreak.
16/n So you can plug your own numbers in and do some informal sensitivity analysis. If you think that the official numbers are about right (say ~5000) and the outbreak started about December 1 (t=58 days), then
R0 = 1 + 0.15*10 = 2.5
R0 = 1 + 0.15*10 = 2.5
17/n If you go with a much bigger number of cases (e.g., theguardian.com/science/2020/j…), sticking with December 1 as the start date, then
R0 = 1 + 0.2*10 = 3
R0 = 1 + 0.2*10 = 3
18/n If you think that the epidemic was actually percolating for month or so before December 1 -- say as early as Oct 15 (t = 105 days) -- and you think there are ~100,000 cases now, then
R0 = 1 + 0.11*10 = 2.1
R0 = 1 + 0.11*10 = 2.1
19/n I guess I've got a lot of new, timely material for my Spring-quarter class, Global Change and Emerging Infectious Disease!
