R naught is the number of cases one case generates

Monday, January 27th, 2020

In epidemiology, the basic reproduction number (denoted R0, r nought) is the number of cases one case generates (on average over the course of its infectious period, in an otherwise uninfected population):

This metric is useful because it helps determine whether or not an infectious disease can spread through a population. The roots of the basic reproduction concept can be traced through the work of Alfred Lotka, Ronald Ross, and others, but its first modern application in epidemiology was by George MacDonald in 1952, who constructed population models of the spread of malaria.


R0 < 1

the infection will die out in the long run. But if

R0 > 1

the infection will be able to spread in a population.

Generally, the larger the value of R0, the harder it is to control the epidemic. For simple models and a 100% effective vaccine, the proportion of the population that needs to be vaccinated to prevent sustained spread of the infection is given by 1 – 1/R0.

Values of R0 of well-known infectious diseases
Disease Transmission R0
Measles Airborne 12–18
Diphtheria Saliva 6-7
Smallpox Airborne droplet 5–7
Polio Fecal-oral route 5–7
Rubella Airborne droplet 5–7
Mumps Airborne droplet 4–7
HIV/AIDS Sexual contact 2–5
Pertussis Airborne droplet 5.5
2019-nCoV Airborne droplet 3-5
SARS Airborne droplet 2–5
(1918 pandemic strain)
Airborne droplet 2–3
(2014 Ebola outbreak)
Bodily fluids 1.5-2.5


  1. Graham says:

    Are those disease names supposed to be Wikipedia links? They currently read as if to internal Isegoria links and give a 404.

  2. Graham says:

    Also, in your notation for vaccination, does the question mark denote Minkowski’s question mark function? [Full disclosure, I had to look that up.]

    You definitely lost me on that one. Not a clue how to use that formula. My vaccination programme must fail.

  3. Isegoria says:

    Sorry about the confusion, Graham. I copied raw HTML code for the table and never went back to clean it up. Also, the question mark comes from WordPress choking on the simple minus sign, which was a proper en-dash, rather than a more common hyphen. Sigh.

  4. Kirk says:

    I think the more important question, right now, is how much we can trust the data coming out of China. That’s going to be what gives the rest of the world the early warning of just what the disease threat is, and there’s no telling what that is, as dishonest as the Chinese government is.

    I forget who it was that first formulated that old trite phrase about “information wants to be free”, but there is a much less well-understood corollary to it all–Information has to be free, in the sense of “transmission”, if you’re going to live in an interconnected and globally communicative world. You can’t have some stretch of it isolated and not transmitting to the rest of it, not if you’re going to have a situation where someone can be in Wuhan today and Seattle before tomorrow morning is out. If you’re going to have a nation like China as a part of the global community, then they absolutely must be transparent and completely honest with the rest of the system, or we risk having these “nasty little surprises” pop up before we know how to deal with them.

    Frankly, the way we ought to be doing this is “Oh, it takes 15 days for you to report there’s a health issue in Wuhan…? Fine; it’s a 16-day wait for you to get out of quarantine at our entry points…”.

    Anything less than that risks suicide on a national scale.

  5. Graham says:


    Thanks. It would be most embarrassing if another of my life programmes were to fail based on a math formula error or misprint. Such a terrible waste of resources and manpower…

    Interestingly, just yesterday I was thinking about some quality control discussions we have here to do with work writing and contemplated reading the rather involved wikipedia articles explaining the hyphen and the various types of dashes. I didn’t but, still, curiously timed.

  6. Graham says:

    Americans, Germans, and Japanese will invent, the Chinese will pirate, introduce and mass produce, the technology to do a full bioscan of every traveller the way we now check for weapons.

    Quick, easy, and the Party now has detailed medical information on everyone in and out of China, and probably remotely from everywhere else with a Huawei infrastructure. Win-win.

  7. Alistair says:

    I saw someone who seemed semi-informed tweeted a 3.8 for the Coronavirus. Is that…confirmed in anyway?

  8. Sam J. says:

    This Coronavirus is odd as can be. I read it has some receptors that are the same as AIDS and it also has part of the body of other different viruses. It’s also fairly strange how the Chinese IMMEDIATELY shut down several whole multi-million population cites. Like they knew what it was right away. How? I expect this thing was engineered and they know it. Either someone planted it in China, (might be the Jews as the Chinese are in no way willing to play their “one world disorder”, “let us control your money supply”, bullshit and they know the future is grim for them when China takes charge), or some idiot at wherever it was made leaked it out of containment somehow. It wouldn’t surprise me a bit if the staff that cleaned up dead experimental bats was selling them to the local open freak food mart they have. Eating bats is fucked up. The Chinese are disgusting. I think their whole civilization is suffering from “post Mao traumatic disorder”.

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