Can you compare probabilities of an epidemic by knowing R0 values? In comparing two diseases with different basic reproduction numbers (R0), is it possible to use the R0 values to calculate the probability of an epidemic spread through a population?
For example, if you compare ebola (R0 ~ 2) to measles (R0 ~ 18), can you say that measles in 9 times more likely to develop into an epidemic? Or 9^2? Or 10^9? Or something more complicated? Or is there no closed-form function way to make that comparison? Is this even a sensible comparison to make?
If this is not the right Stack Overflow site to post this to, could you please point me in the right direction? Thanks!
CONTEXT
I am much more afraid of an unvaccinated measles epidemic than an ebola epidemic, and I'm trying to explain why to some friends - inspired by this graphic that appeared in today's Guardian blog:
http://www.theguardian.com/news/datablog/ng-interactive/2014/oct/15/visualised-how-ebola-compares-to-other-infectious-diseases
I'm pretty good at stats (mostly self-taught-on-the-job), but my epidemiology knowledge consists of Bio 101 in college, reading And The Band Played On, and briefly dating a med student studying it.
If you're not familiar with R0, it's a dimensionless measure that measures how many people will become infected, on average, from a single case.* As always, Wikipedia has a good introduction with references:
https://en.wikipedia.org/wiki/Basic_reproduction_number
( * ) Note: In writing that, it occurs to me that it that definition probably implies that it's exponential, so a disease with R0 = 18 should be on the order of (constant)*(10^9) times more likely to spread?
 A: Hmm, well for starters, that infographic is pretty, but it rather simplifies things, for better or worse.
R0 is just one of several parameters that govern the dynamics of disease spread. And even it is misleading as an average. Take, for example, HIV, which is transmitted at a higher rate from men (both to women and other men) and a lower rate from women (both to men and other women). The statistical number of new infections from a single person (R0) really depends on the person's sex -- or for a population, on the sex ratio. But it's not linear, so you can't just do an arithmetic mean if you know the R0 for subsets of the population. Moreover it depends also on behavior (number and sex of sex partners, needle use, having babies). So coming up with an average R0 is both really tricky and subject to fast modification based on social structure change as well as behavior change.
The concept of R0 works best for what are termed "well mixed" populations, meaning that every individual has an equal chance of coming into contact with each other individual. This is a mathematically useful assumption, and can sometimes be a good enough approximation. But for large scale human diseases, the assumption is obviously violated.
It also assumes that an unvaccinated and non-immune (termed "naive") population -- at least on that infographic. The goal of vaccination programs is to reduce R0 to below 1, i.e. below replacement. If the average infected individual infects fewer than 1 other, the disease will die out.
You'll also notice that some of those diseases are vectored (Lyme, e.g.), and some (like tuberculosis) have a complex manifestation as a disease. This further violates the well mixed population assumption.
Also, you use the word "epidemic", which typically implies a rapid spread of the disease. Some diseases hang out in individuals for a long time and spread relatively slowly (like tuberculosis). That R0 tells you the lifetime exposure to others based on the length of infectiousness. A disease that has an R0=10, but infects those 10 people over a decade is not likely to cause an epidemic. Instead, that disease will be deemed "endemic", meaning that it has a high enough R0 that it will spread to everyone, but not very quickly. These diseases tend to have relatively stable proportion of individuals infected, as old infected individuals die or become immune and new susceptible individuals are born.
So... if you have two diseases that have different R0 values and transmit at the same rate and don't manifest in a complex way and you have a really truly naive well-mixed population, then you can specify the relative rate (exponential, like you said) at which the two diseases spread through the population.
Which, I should note, is not the same thing as the probability of an epidemic. In the case I describe, the probably of an epidemic for both diseases (assuming a fast enough rate of transmission) is 1.
The probability of an epidemic for a real disease in our messy world is going to have to do more with immunity, social contact patterns, the particular manifestation of the disease, and the means of transmission.
A: I'm going to address a couple different aspects of your question, but the short answer is "No".


*

*First, on probability: R0 is a tricky thing to think about in terms
of probability, because it isn't a probability. Generally speaking,
it's estimated using a deterministic model.

*Second, you have to keep in mind that R0 is something of a idealized parameter - the number of secondary cases caused by a
primary case in an entirely susceptible population. For measles,
that's essentially describing Fantasyland, whereas for Ebola it is at
least a marginally more reasonable scenario to consider. That makes
the R0 between diseases difficult to compare.

*Third, R0 is contextless. Epidemics are not. To use a somewhat extreme example, if a population is 100% vaccinated against measles, the R0 could be 1.8, 18 or 180 and it wouldn't matter.


What this all boils down to is a number that, despite the attention it gets, is somewhat limited in what it can actually do. You have to take the context of a disease into account, and consider it from there. For example, while large populations behave the way deterministic models predict they will (though I'll note "large" needs to be quite large), smaller populations are highly subject to stochastic extinction, which does strange things to the behavior of epidemics. Similarly, there is a readily available, easy to use vaccine for measles, and no such vaccine for Ebola, so if you want to talk about true epidemic potential, you don't only have to talk about the "launch" of the disease (which is where R0 is focused) but how well you can bring it under control.
There are simulation approaches that use estimates like R0 to predict the probability of an outbreak, and then nature of that outbreak, but it's very difficult to justify just going off R0. What you can predict using R0 however is both the critical above or below 1 threshold, and that measles for example is more transmissible in a hypothetical epidemic than Ebola, though again I'd assert the context for both epidemics would change the nature of things more than their R0 (see how much we freaked out about a single-digit number of Ebola cases vs. MMR vaccine denialism).
