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I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical models that are used to predict the spread, mathematical studies of effectiveness of various strategies, etc.

*(Added) By old I also mean well-established models.

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    $\begingroup$ Out of respect though , if this question was asked by someone anonymous it will be closed in seconds . $\endgroup$
    – bambi
    Commented Mar 3, 2020 at 19:30
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    $\begingroup$ Mathematically, I doubt that there's anything particularly new about this coronavirus. Mathematical models of epidemics are well-established. Of course we'd like to know the parameters (and to what extent something can be done about them). See Wikipedia $\endgroup$ Commented Mar 3, 2020 at 19:30
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    $\begingroup$ There are many. Here is a recent article of my friend: bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-3-19 $\endgroup$ Commented Mar 3, 2020 at 21:34
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    $\begingroup$ @MarkSapir I have to disagree - I think this question is simply far too broad for MO. (I won't vote to close because I have absolutely no background in the relevant topic, however.) $\endgroup$ Commented Mar 4, 2020 at 1:30
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    $\begingroup$ Glenn Webb is a very good mathematician. I am sure he knows everything there is to know about the subject. You may want to ask him your questiom directly. $\endgroup$
    – user6976
    Commented Mar 4, 2020 at 15:08

8 Answers 8

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There is the whole discipline of math models of epidemics.

See, for example, Fitzgibbon, William E.(1-HST); Morgan, Jeffery J.(1-HST); Webb, Glenn F.(1-VDB); Wu, Yixiang(1-VDB) Spatial models of vector-host epidemics with directed movement of vectors over long distances. (English summary) Math. Biosci. 312 (2019), 77–87

and the references there.

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    $\begingroup$ Thanks for the answer, Mark! $\endgroup$
    – Gil Kalai
    Commented Mar 4, 2020 at 14:11
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Maybe relevant:

Yu Chen, Jin Cheng, Yu Jiang, Keji Liu, A Time Delay Dynamical Model for Outbreak of 2019-nCoV and the Parameter Identification, https://arxiv.org/abs/2002.00418

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    $\begingroup$ Thanks for the answer, Martin! $\endgroup$
    – Gil Kalai
    Commented Mar 4, 2020 at 14:11
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The following paper is a little strange, since it dates back to 2015, but has some valuable data:

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    $\begingroup$ Here is another case from february 2019 "Bat Coronaviruses in China" from the abstract "Thus, it is highly likely that future SARS- or MERS-like coronavirus outbreaks will originate from bats, and there is an increased probability that this will occur in China." $\endgroup$
    – Dabed
    Commented Mar 14, 2020 at 19:02
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    $\begingroup$ @Daniel D. And it is more strange why we do not have any kind of vaccination by these predictions!? $\endgroup$
    – Shahrooz
    Commented Mar 14, 2020 at 19:05
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    $\begingroup$ There exists the "Coalition for Epidemic Preparedness Innovations (CEPI)" which was created after the Ebola outbreak and is leading the efforts in the creation of a vaccine but is not the only one so there are a lot of news and I would say is not clear were this race is going yet, on the other hand for MERS there was no vaccine either so it seems to me what was done first was to test if the treatments for MERS were also effective against COVID-19 in particular Remdesivir and chloroquine $\endgroup$
    – Dabed
    Commented Mar 14, 2020 at 20:13
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    $\begingroup$ For completeness sake let me add a another paper that I have read on the news more or less had foreseen the situation:Severe Acute Respiratory Syndrome Coronavirus as an Agent of Emerging and Reemerging Infection $\endgroup$
    – Dabed
    Commented Apr 14, 2020 at 23:23
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The book by Gábor Csárdi, Tamás Nepusz, Edoardo Airoldi, Statistical Network Analysis with igraph

Based around popular software library igraph, Wikipedia link contains whole chapter with source codes (in R) on Epidemics on networks in particular 6.5 Vaccination strategies

Let me quote the content of the chapter:

6 Epidemics on networks
6.2  Branching processes
6.3  Compartmental models on homogeneous populations
6.3.1  The susceptible-infected-recovered (SIR) model
6.3.2  The susceptible-infected-susceptible (SIS) model
6.3.3  The susceptible-infected-recovered-susceptible (SIRS)model
6.4  Compartmental models on networks
6.4.1  A general framework for compartmental models onnetworks
6.4.2  Epidemics on regular and geometric networks . . . . . . . . 180
6.4.3  Epidemics on scale-free networks . . . . . . . . . . . . . . . . . . . 187
6.5  Vaccination strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
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    $\begingroup$ Thanks for the answer, Alexander! $\endgroup$
    – Gil Kalai
    Commented Mar 11, 2020 at 6:46
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Here is a recent paper written by mathematicians: Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China.

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  • $\begingroup$ Thanks for the answer, Matt! $\endgroup$
    – Gil Kalai
    Commented Mar 11, 2020 at 6:45
  • $\begingroup$ @GilKalai: My name is not Matt (and I wrote this answer), but thanks nevertheless. $\endgroup$
    – GH from MO
    Commented Mar 11, 2020 at 14:17
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    $\begingroup$ Thanks for the answer, GH from MO! $\endgroup$
    – Gil Kalai
    Commented Mar 11, 2020 at 15:58
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Recently found this :

https://staff.math.su.se/tom.britton/

Maybe relevant.

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    $\begingroup$ Here is a related videotaped lecture by Britton, youtu.be/gSqIwXl6IjQ $\endgroup$
    – Gil Kalai
    Commented Mar 14, 2020 at 18:19
  • $\begingroup$ @GilKalai Wow , thanks , I didn't know about video $\endgroup$
    – bambi
    Commented Mar 14, 2020 at 18:20
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The following paper is extremely important because it has informed the decisions of the UK government that realised (announced) on Monday 16/03/2020 that it can not afford "Herd immunity". The paper only shows the outcomes of the model and speaks about its parameters. It would of course be extremely interesting to know what exactly is the mathematics behind it. Mathematicians should try to read it.

https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf?fbclid=IwAR2Ca5Ki23DWn-EGWeB3yaNE4f9GmnUcEWU_S60lsDC230AKUg4v_w82qeE

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  • $\begingroup$ Thanks for the answer, aglearner! $\endgroup$
    – Gil Kalai
    Commented Mar 21, 2020 at 19:21
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    $\begingroup$ Here is a related mathematical discussion on Gowers' blog: gowers.wordpress.com/2020/03/28/… $\endgroup$
    – Gil Kalai
    Commented Apr 1, 2020 at 21:09
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Volume 12 of What's Happening in the Mathematical Sciences by Dana Mackenzie has three chapters devoted to mathematical modeling related to the coronavirus pandemic.

Fifty Ways to Beat a Virus (Part 1)
In 2020, the world for the first time in a century confronted a global pandemic that would claim millions of lives. While students were sent home and campuses closed, many mathematicians found an opportunity to join the fight against COVID-19. Even simple differential equation models can teach us important lessons about the exponential growth of a new epidemic and the importance of threshold behavior. Using more elaborate (and realistic) models, two mathematical modeling groups, in Texas and Illinois, had a profound and positive effect on the management of the epidemic by local and state authorities during the first waves.

Fifty Ways to Beat a Virus (Part 2)
Continuing the previous chapter, Part 2 discusses the problems confronted by mathematicians and epidemiologists in the later part of 2020 and in early 2021. How could universities re-open safely? How does the uncontrolled spread of an epidemic in prisons affect the surrounding community, and what can be done about it? And the biggest question: could vaccination bring the epidemic under control? Even though the coronavirus kept throwing surprises at us, mathematicians did a surprisingly good job of developing strategies, giving realistic answers and highlighting the main reasons for uncertainty.

Fifty Ways to Beat a Virus (Part 3)
Another important front in the battle against COVID-19 was to understand how the infection progresses within the human body. Why do some people have life-threatening symptoms, while others have none at all? An online group called the “Immune Gals” highlighted the delayed release of interferon as a characteristic marker of severe cases. Another mathematician used the tools of graph theory to identify parts of the viral RNA that are especially vulnerable to attack by drugs or gene therapy. And a third group adapted a machine-learning language model to detect escape variants of coronavirus. In effect, they taught the computer to “speak virus.”

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