Talk:Basic reproduction number

Initial comments

A comment on: "In particular, the proportion of the population that needs to be vaccinated to provide herd immunity and prevent sustained spread of the infection is given by 1 − 1/R0." Herd-immunity is not something that appears at a certain level of vaccine coverage. Infectious disease dynamics are non-linear, to varying degrees depending on R0, at all levels of vaccination. "to provide herd immunity and" should be omitted as it misleads the reader into thinking that vaccination only benefits vaccinated individuals until a certain threshold is crossed, and past that we start observing aggregate-level protection. 72.65.139.162 (talk) 15:57, 17 May 2010 (UTC)

some patent nonsense corrected: R0 is defined in the absence of internventions; R0 for SARS can't have been less than 1, otherwise epidemics would never have started (I think the *effective* or *net* repro number, Rt, is meant - would be worth mentioning that, but I haven't) Also R0>1 doesn't guarantee a major epidemic , it just makes it possible. We also need the word "mean".

This bit is also nonsense "If :R₀ = 1, then the infection will become endemic in the population." In reality R will never be 1, so it is irrelevant. In a stochastic model if R is one extinction will occur within a short time. Deterministic models are fine as approximations to stochstic models for large populations, but a population of 1 case is not large, and the deterministic result is irrelevant.

>>Just learning about this at university now. The way we're taught Ro<1 disease dies off/fails to spread, Ro=1 disease stays constant/endemic, Ro>1 disease spreads/epidemic. I understand how Ro will never realistically be 1, but mathematically it's a very valid concept. Shouldn't the wikipedia entry properly convey the mathematical concept that validly explains Ro=1 as well as (if not more so than) anecdotal data which suggests Ro can't be 1? --98.192.35.52 (talk) 00:00, 16 March 2011 (UTC)

Also, remember this stuff applies equally to animals and plant, so I cut out words like "people".

Generally true that higher R0 makes control harder (though ohter factors come into play) and stuff about herd immunity threshold added.

Stuff on course of epidemics is irrelevant (why stop at SIR - what about SIS, SIRS etc. R0 applies to all).

Should we list sources for R0 estimates? If so, It's Mills, Nature 2004 for R0 for flu, Wallinga, Am J Epidemiol 2004 for SARS (though not strictly R0..more Rt). Anderson & May quote numbers for AIDS and mealses (though not sure if they are the same as those quoted. Generally people quote different values for subsaharan AFrica and elsewhere, adn of course wide variation possible in different groups - so best to say what population R0 is quoted for. Worth adding, maybe).

What about history? Shouldn't we mention history of R0? Kermack Mckendrick, Ross et al? And what about the Heesterbeck formulation for heterogeneous populations (the reason we need the word "typical"). Heesterbeck (who's PhD was titled R0) gives a great lecture including history of R0 (and the other names it's gone by, before Anderson & May popularized R0), and should probably mention his work here. All worth doing if anyone's got the time...

Other points: Why there is a separate definition for basic reproduction number and basic reproductive rate (http://en.wikipedia.org/wiki/Basic_reproductive_rate)? As far as I know they are just different names for the same concept. Now, if there is a difference between terms that I am not aware of, the reader can not tell by reading both articles. I agree that it would also be nice having a definition for Rt. That's my 2 cents anyway!

"By definition R0 cannot be modified through vaccination campaigns." Can this be explained more clearly in terms of what it means for a pandemic virus? — Preceding unsigned comment added by Carusus (talk • contribs) 18:09, 12 March 2020 (UTC)

Uncertain reference

I doubt the reference cited for the reproduction range of HIV/AIDS as 2-5. The reference cited is from 1979, and transmission studies by Koopman and others were published at least 10 years later. 66.229.140.215 (talk) 13:35, 29 December 2007 (UTC)

The R0 for HIV/AIDS has been popping up in media coverage (e.g. here and here) and other online discussion re COVID-19, and the source for these figures seems to be this Wikipedia article. I was also curious about the HIV/AIDS R0 info in the chart, sans references, which brought me to this topic on the talk page. I have three comments and a question:

(1) Current references that explicitly state the R0 for HIV/AIDS are sparse, I’ve found none, perhaps it’s buried somewhere in science journals, but I haven’t been able to tease it out, this is not my field either. All I’ve found are articles that discuss how to calculate R0 for HIV/AIDS without actually specifying what the R0 for HIV/AIDS is. However, another reason seems to be that calculating an exact R0 is quite challenging hence the title of the following article: Delamater, P. et al. 2019. Complexity of the Basic Reproduction Number (R0). Emerging Infectious Diseases. 25.1. 1-4.; further, the concluding remarks in the following article state: “During the last twenty years Ro has emerged as a basic concept in infectious disease epidemiology, but it has also become apparent how difficult it is to apply in actual field situations” Dietz, K. 1993. The estimation of the basic reproduction number for infectious diseases. Statistical Methods in Medical Research. 2. 23-41.

(2) Noting above comments from 66.229.140.215 and others, references such as Koopman and Anderson & May (which are mentioned in the talk section, not cited in the main article) certainly are decades old; however, Koopman and Anderson & May are cited with approval in more recent scholarship, including: Delamater 2019 (above), Nah, K., et al. 2017. Test-and-treat approach to HIV/AIDS: a primer for mathematical modeling. Theoretical Biology and Medical Modelling. 14. 1-11.; Bonacci, R. and Holtgrave, D. 2016. Evaluating the Impact of the US National HIV/AIDS Strategy, 2010–2015. AIDS and Behavior. 20. 1383-1389; Holtgrave, D. 2010. Is the Elimination of HIV Infection Within Reach in the United States? Lessons from an Epidemiologic Transmission Model. Public Health Reports. 125. 372-376.; Déirdre Hollingsworth, T., et al. 2008. HIV-1 Transmission, by Stage of Infection. Journal of Infectious Diseases. 198. 5. 687–693.

(3) The closest I’ve come to an answer to current figures for HIV/AIDS R0 is from personal correspondence with Holtgrave (03/02/2020) where he states, based on estimates from his 2010 article (above): “At the current transmission rate of roughly 3.5 in the US, this would imply Rsub0 values in the range of 1.01 to 1.31 (for a variety of estimates of infectiousness duration). This indicates that the HIV Rsub0 is likely still over unity in the US, but getting closer to the bright line of Rsub0 equaling unity.” Of course, without a forthcoming article, this doesn't work as a reference for HIV/AIDS R0 in the chart on the R0 Wikipedia article.

(4) Is it possible to include in the Wikipedia R0 article how R0 relates to attack rate, infection rate, and transmission rate? — Preceding unsigned comment added by 2602:302:D154:79A0:5844:C284:64F3:D46F (talk) 10:17, 3 March 2020 (UTC)

Reproductive rate

Reproductive rate lands one here, but this article doesn't explain it. Could s.o. start a separate page (for all organisms please, not just for humans or pathogens!) or put a paragraph here. THANKS76.97.245.5 (talk) 16:40, 6 April 2009 (UTC)

Reproduction ratio

The correct term, according to Diekmann et al (1990) is the basic reproduction ratio, since R0 does not have a dimension (it is cases per case), so it is certainly not a rate. Should/can we change the page title? SpaceLem (talk) 12:50, 12 September 2012 (UTC)

Spelling of R naught?

Does anyone happen to know why it's R naught instead of R nought? I always understood that "naught" means nothing and "nought" means zero. It's not a mistake in the article, because I have seen (and been puzzled by) the same spelling elsewhere.79.103.108.162 (talk) 20:28, 1 February 2016 (UTC)

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Disambiguation

We need to clarify the triad of epidemiological R's:

1. R_0 = τ/γ, a quantity describing the dynamics of disease progression under the SIR model, specifically the ratio of the frequency of infection events (τ) to the frequency of recovery events (γ). This is not the transmissibilty of the disease - it is a model parameter.
2. R = R_0*χ, the transmissibility of the disease. χ is the susceptible proportion of the population.
3. R(0) is the number of recovered at time t=0 in the SIR model.

Thoughts on new sections on the page? — Preceding unsigned comment added by Ekalosak (talk • contribs) 06:44, 31 January 2020 (UTC)

Merge with Net reproduction rate

This is exactly the same principle as net reproduction rate (also abbreviated as R₀), just applied to a different field. The basic reproduction number article already contains information about population ecology that actually corresponds to net reproduction rate. Although the "net reproduction rate" article is written as if it only applies to human demography, this term is widely used in population ecology, e.g. at Brittanica: [1] Bueller 007 (talk) 04:21, 2 February 2020 (UTC) This may not be such a good idea as infection and reproduction use quite different concept once you go into details - see the above remarks about Disambiguation. In reproduction of non-parasites, there is no incubation period, no disease progression etc. — Preceding unsigned comment added by Gerard Widerot (talk • contribs) 22:30, 3 February 2020 (UTC)

Smiley Face

Patient zero in this image is happy. I understand that patient zero for each disease is in fact sick and so would probably be unhappy like all the other people who caught it. I recommend making the circles blue with a sad face. Robert Brockway (talk) 00:41, 15 February 2020 (UTC)

How about R0 of COVID-19 ?

At present it is writen '1.4–3.8', but a week and some day ago it was '1.4–6.6'. It is not stablized. --Kyuri1449 (talk) 19:25, 1 March 2020 (UTC)

I noticed this too and while I'm in virtually no mood to go seek out some sources, there was one paper that the "6.6" value linked to that said :that the value was between 4 and 6 roughly. It isn't 100% stabilized and most of the information is just unknown/not researched enough yet. --Prezi2 (talk) 09:33, 4 March 2020 (UTC)

"THE" Ro of COVID-19, or of any desease for that matter, does not exist. The Ro locally measured in Wuhan at the beginning of the epedimic was averaged at 2.2 within a 90% rate of certainty between 1.4 and 3.8. The Ro will differ between localities, and thus between countries. It all has to do with how close people make contact, with how many different people they make close contact and how mobile they are. It might well be that the Ro in a develeoped county like the Netherlands can run up to 3.5. especially at the start of the epedemic. Since the Netherlands are highly populated, highly mobile, highly international and often greet kissing each other. Special measures may temporarily lower the Ro, but since all special measures will (have to) end finally, so will this temporal reduction of the Ro77.60.121.89 (talk) 12:47, 18 March 2020 (UTC)

Inconsistent use of γ

Here γ is used as infectious period (which leads to $R_{0}=\beta \gamma$), but in Compartmental models in epidemiology it is used as the inverse of that period (which leads to $R_{0}={\frac {\beta }{\gamma }}$). Is one of them wrong? Or do different authors use different definitions? Anyway, this is a confusing situation. --mfb (talk) 01:23, 11 March 2020 (UTC)

Even the description is inconsistent. The denominator is described as the infectious period, and that by decreasing it the R0 value will be lower. This is patently impossible. In section 3 The basic reproduction number the equation is described as a product of the two values. Pekkapihlajasaari (talk) 13:02, 28 March 2020 (UTC)

Inconsistent math

Section "Reproductive number as it relates to contact rate and infectious period" reads "This simple formula suggests different ways of reducing R0" .. "It is also possible to decrease the infectious period γ by finding and then isolating, treating or eliminating".

PROBLEM: With $\gamma$ as the denominator, decreasing it will increase $R_{0}$, which is not desirable. As a previous comment made, Frequency and Period are inversely related. Which one is being used here? --RSH (talk) 18:44, 19 March 2020 (UTC)

Graphs in embedded video...

Two comments:

1. The first plot at 9:10 minutes, "# OF CASES vs TIME SINCE FIRST CASE" makes the point about not exceeding the Healthcare System Capacity, but implies that there are about 9% more "Events" (deaths, total cases, ???) with the protective measures, because the area under the red curve is about 0.91 x the area under the blue curve. May need a discussion to qualify a little better, perhaps some real data from several pathogens addressing this.

2. The second graph at 9:32 minutes, "DEATH RATE/100,000 POPULATION vs EXCESS ... MORTALITY" can't be compared with the first graph because its ordinate is "RATIO OF DEATHS," while the ordinate of the first graph is total events. The area under the red curve is about 2.3 x the area under the blue curve, but I'm not sure integrating ratio of population over time is even meaningful. And it certainly can't be compared to the first plot, because one is deaths by fraction of population and the other is total (but undefined) events.

SixtyRedDevil (talk) 00:48, 25 March 2020 (UTC)

Link to a graph in the embedded video

There is a chart/graph in the video, shown at about 7:30 till 7:43, with a link to London School of Hygiene & Tropical Medicine's Centre for the Mathematical Modelling of Infectious Disease (CMMID)'s GitHub page with that same chart and more data, probably more recent:

 https://cmmid.github.io/topics/covid19/current-patterns-transmission/global-time-varying-transmission.html#summary-of-latest-reproduction-number-and-case-count-estimates

(The tab titled "Summary of latest reproduction number and case count estimates" needs to be clicked to reveal the chart; doesn't seem to scroll/show automatically.)

Shall this be somehow added in the article?

(Don't know how, or if, the video is related to the CMMID page.) — Preceding unsigned comment added by 31.183.172.66 (talk) 03:46, 25 March 2020 (UTC)

"Disease reproduction number"

I've seen the phrase "disease reproduction number", apparently with the same meaning, e.g. here [2]. Should we set up a redirect from Disease reproduction number to this page? Lfh (talk) 08:33, 25 March 2020 (UTC)

Given that it is not in the glossary of terms[3], I would say no.. BiologicalMe (talk) 15:04, 25 March 2020 (UTC)

Wikilink to effective reproduction number .. redirects back here

The overview section links to effective reproduction number which comes back here. Either there should be a stub article for that or the wikilink should be removed or made just in-page? Richiez (talk) 20:30, 30 March 2020 (UTC)