# Relevant mathematics to the recent coronavirus outbreak

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.

• Out of respect though , if this question was asked by someone anonymous it will be closed in seconds . Mar 3 '20 at 19:30
• 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 Mar 3 '20 at 19:30
• There are many. Here is a recent article of my friend: bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-3-19 Mar 3 '20 at 21:34
• @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.) Mar 4 '20 at 1:30
• 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.
– user6976
Mar 4 '20 at 15:08

## 8 Answers

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.

• Thanks for the answer, Mark! Mar 4 '20 at 14:11

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

• Thanks for the answer, Martin! Mar 4 '20 at 14:11

The following paper is a little strange, since it dates back to 2015, but has some valuable data:

• 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." Mar 14 '20 at 19:02
• @Daniel D. And it is more strange why we do not have any kind of vaccination by these predictions!? Mar 14 '20 at 19:05
• 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 Mar 14 '20 at 20:13
• 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 Apr 14 '20 at 23:23

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• Thanks for the answer, Alexander! Mar 11 '20 at 6:46

Here is a recent paper written by mathematicians: Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China.

• Thanks for the answer, Matt! Mar 11 '20 at 6:45
• @GilKalai: My name is not Matt (and I wrote this answer), but thanks nevertheless. Mar 11 '20 at 14:17
• Thanks for the answer, GH from MO! Mar 11 '20 at 15:58

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

• Thanks for the answer, aglearner! Mar 21 '20 at 19:21
• Here is a related mathematical discussion on Gowers' blog: gowers.wordpress.com/2020/03/28/… Apr 1 '20 at 21:09

Recently found this :

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

Maybe relevant.

• Here is a related videotaped lecture by Britton, youtu.be/gSqIwXl6IjQ Mar 14 '20 at 18:19
• @GilKalai Wow , thanks , I didn't know about video Mar 14 '20 at 18:20

The AMS has made available 4 books related to epidemics:

"Free AMS mathematical modeling books and journals during COVID-19 pandemic"