Talk:Compartmental models in epidemiology

Why does the basic reproductive rate/number have a negative sign in front of it? R_0 is supposed to be positive. Lambda and delta are both positive constants.....

Equation for Final Recovered Number

In the section for the "SIR model without vital dynamics" it seems like

$R_{\infty }=1-S(0)e^{-R_{0}(R_{\infty }-R(0))}$

should be

$R_{\infty }=N-S(0)e^{-R_{0}(R_{\infty }-R(0))}$

since earlier in the section it was stated that

$S(t)+I(t)+R(t)=Constant=N$

opposed to when $N=1$ where

$S(t),I(t),R(t)$

are the proportion of the population that are in that state. KNesHere (talk) 02:10, 10 February 2010 (UTC)

Add labels to diagram.

Adding labels to the red, green, and blue plots would help explain what that plot is showing. —The preceding unsigned comment was added by 74.118.13.168 (talk) 03:22, 1 May 2007 (UTC).

The label colors do not match those of the plots. Yellow for Blue is annoying, but reversing the roles of Red and Green is conducive to misunderstanding.

Needs attention of expert

I'm just a layman here, and this may sound an odd question, but how are these formulas used? Just for kicks I tried to make sense of how they might be used in a measuring an outbreak of flu, cholera, or zombies, but all I get is "For the full specification of the model, the arrows should be labeled with the transition rates between compartments." but what does that even mean? An example case or two would be nice. —Preceding unsigned comment added by 205.206.107.136 (talk) 06:29, 21 October 2010 (UTC)

An example of use would be for instance the H1N1 outbreak and the time it took for Governments to get emergency vaccination programs in place. If you wait for too long of a period to vaccinate,a vaccination program may be futile in terms of reducing the total people in the population that gets infected. Other uses may include knowing what demands to expect in Hospital Emergency rooms so that hospitals can staff doctors and nurses accordingly. Back to the H1N1 example in some cities in Canada there was a 2 month delay in the vaccination program that was rolled out, this resulted in a 60% infection of the populations instead what would have been closer to 25%. These models can also tell us what proportion of the population needs to be vaccinated in order to complete eliminate a disease from the population. Some diseases are not virulent enough to exist in populations that are 60% vaccinated against it however there are other diseases that survive in populations with 99% vaccination. These models tell us these things.

The transition rates are how many people at each "time step" move from being susceptible to infected or from infected to recovered. for the ds/dt equation the negative term is the amount of susceptible moving to infected at each time step. You'll notice that the same amount is added to teh di/dt equation. —Preceding unsigned comment added by 99.225.12.152 (talk) 11:44, 24 November 2010 (UTC)

Needs attention of an expert whose native language is english. The article has lots of grammatical errors - to the point where I'm unable to make sense of a number of statements. --66.41.154.0 (talk) 03:48, 23 September 2014 (UTC)

I've tagged the article. It isn't just that it needs to be rewritten in plain English, some of these changes need to be verified. SW3 5DL (talk) 12:58, 23 October 2014 (UTC)

Parts of this article definitely seem really wrong, particularly some of the equations and stuff about the SIR model. Just visited it in preparation for an epidemiology exam, and I have a textbook in front of me contradicting a lot of this page. (Modeling infectious disease in humans and animals, Matt J. Keeling and Pejman Rohani - may help others). I'm not enough of an expert to fix it, although perhaps in a few weeks I'll give it a shot. Whole page needs a comprehensive review rhodesj971 (talk) 10:57, 3 May 2015 (UTC)

Thanks for pointing that out. It's probably down to vandalism. Science, math, biology, etc usually suffer the most because editors on page patrol are not familiar with the topics and can't recognize that the charges are detrimental. Good luck with your exam. SW3 5DL (talk) 14:24, 3 May 2015 (UTC)

Need to redo the Bibliography

To make this article accessible, we need to reduce the size of the bibliography. I see a lot of very specific articles that are place there but not used to validate any claims in the main body of the article. I think therefore we should remove those which are not used, and cite some more broad text book resources, or cornerstone research articles in the field.

Thoughts? 149.171.172.161 (talk) 04:46, 21 October 2014 (UTC)

Maybe you could list here the ones you'd remove and add. SW3 5DL (talk) 12:48, 23 October 2014 (UTC)

Have already started, although only have done one for now. 149.171.172.161 (talk) 00:04, 24 October 2014 (UTC)

Delete the lot, I say. The only ones I think are of general relevance are Anderson + May's book, and the Kermack-McKendrick article, and they're both in the references anyway. Most (all?) of the bibliography was added by a single editor in 2008, who I suspect was just dropping in a paper or thesis they wrote. Adpete (talk) 03:09, 2 March 2018 (UTC) Done. Adpete (talk) 03:19, 2 March 2018 (UTC)

Merger proposal

This article covers much of the same ground as Epidemic model. I think that they should be merged, and have stated so in the other article's talk page.

I have added the tags for this. I agree, although Mathematical_modelling_of_infectious_disease is also very similar and "epidemic model" is more general than just compartmental models, although that is largely what it covers. I suggest maybe some of the historical/other non-compartmental content in epidemic model actually go into mathematical modelling of infectious disease instead of here. Mvolz (talk) 17:29, 26 June 2017 (UTC)

External links modified (January 2018)

Hello fellow Wikipedians,

I have just modified one external link on Compartmental models in epidemiology. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20091120223448/http://www.math.uiowa.edu/~hethcote/PDFs/1976MathBiosci.pdf to http://www.math.uiowa.edu/~hethcote/PDFs/1976MathBiosci.pdf
• Added {{dead link}} tag to http://bill.srnr.arizona.edu/mss/UPD-1%20Published.pdf

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 05:45, 23 January 2018 (UTC)

Major cull

I deleted 2 entire sections, and most of the bibliography. This was added by a single user in 2008, and reads suspiciously like a paper or project they wrote. More importantly, it was off topic. The section "Modelling mass vaccination programmes" is not about compartmental models, but about one (of many) applications of compartmental models, and there's no reason given why that application in particular should be in the article. The section "The influence of age: age-structured models" is going a step beyond compartmental models, but again no reason is offered why to take this extension in particular. Then most of the bibliography was deleted because it was very specific to those two topics. I won't protest if someone sees fit to restore these sections (last version is here [1]) but I think it's inappropriate for a general article, and was cluttering it. Adpete (talk) 01:51, 3 March 2018 (UTC)

@Adpete: I mean, the reason to take that extension in particular is that modelling vaccination strategies is practically the entire function of epidemiological models to begin with :). But I agree the section as written is not very good; are these text book models? Where do they come from? How do they compare to other published models, of which there are many? But I think rather than deleting it should be fixed. At any rate, it's not an application of a model, so this is why I reverted. It IS a model. Applying a model involves showing how predictive a model is with real data. So theoretically speaking, it belongs in the article. Mvolz (talk) 09:35, 1 July 2018 (UTC)

Yes but there are probably thousands of papers which apply compartmental models in different ways. Why should this application make it into the article, and not all the others? That is my concern. Especially the very detailed "The influence of age: age-structured models" section. Adpete (talk) 13:03, 1 July 2018 (UTC)

Inconsistent use of γ

Here γ is used as inverse of the infectious period (which leads to $R_{0}={\frac {\beta }{\gamma }}$), but in Basic reproduction number it is used as that period (which leads to $R_{0}=\beta \gamma$). Is one of them wrong? Or do different authors use different definitions? Anyway, this is a confusing situation. --mfb (talk) 01:24, 11 March 2020 (UTC)

RfC: consistency of definition and use or symbol R

In the article, at some points the symbol R is used for the recovered, at other points it is used for the recovered and the deceased. I suspect there may be conditions or assumptions under which no essential mathematical difference arises from this inconsistency. But I prefer to have the definitions clear, and their use consistent. So, could we agree to sticking to defining and using R for recoveries only?Redav (talk) 16:00, 19 March 2020 (UTC)

Birth Rate

Both in the SIR section with vital dynamics and, since it was changed by some IP to be that way, and in the SEIR section, the birth rate $\Lambda$ is a constant term, independent of the population size. To me it is unclear why that should be the case. Can anyone comment on this? Cheers --Sensorpixel (talk) 22:31, 21 March 2020 (UTC)

Constant population

In the section about the SEIR model, it says: "We have S + E + I + R = N, but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general N is a variable." Isn't a better justification for this lack of demography a separation of timescales: disease dynamics being much faster than population dynamics so that a quasi-steady state is an accurate approximation? --OpenScience (talk) 11:29, 22 March 2020 (UTC)

Also, the section says: "vital dynamics with birth rate Λ equal to death rate μ". This is cannot be correct because form the equations it is clear that μ is a per capita rate, measured in units of 1/time, whereas Λ is measured as individuals per unit of time. OpenScience (talk) 12:43, 22 March 2020 (UTC)