## Coronavirus pandemic model

wg48temp9 - 13-4-2020 at 12:18

I found a model for the pandemic on Semantic Scholar
see Attachment: corvir-model-4c6ac7af8e7681ac8d7804f9b63fab2d8e27.pdf (117kB)

Its mathematically simple growth model using basic reproduction parameter R. I would have expected most governments to be using a more complicated model but I guess with populations of millions it works sufficiently well to produce the graphs for the politicians. Below is a graph from the paper.

PS: I am interested in a model that shows the long term infection/death rate. I guess it would have to include a finite population, a decreasing R as the population become resistant and a sub population of super spreaders.

[Edited on 4/13/2020 by wg48temp9]

Chemorg42 - 13-4-2020 at 14:12

A growth model!?, Really?
I would have thought an agent based model running on a powerful processor would be more accurate in simulating Covid19's particular characteristics. However, I guess that the accuracy of such a system breaks down as population size increases.
I myself considered creating a simulation to model the spread through a crowd (using 2m radius, occasional "Discharges" of infectious material from the infected, and other statistics I have not found.) Just an idea.

j_sum1 - 13-4-2020 at 14:39

3blue1brown

Basic explanation of a simple model and the parameters that are critical in describing a pandemic
https://youtu.be/Kas0tIxDvrg

Simulation and analysis of more realistic scenarios and illustrating the effect of modifying human behaviour.
https://youtu.be/gxAaO2rsdIs

Presumably the models being used to inform government policies are more sophisticated than this but they will also be very susceptible to minute changes and the effect of randomness. In other words, the mathematical models can be scarily close to real data but the situation is still chaotic (mathematically).
Anyway, these videos are both excellent and worth the half hour or so to watch.

### It's all seriously cooked data

sodium_stearate - 13-4-2020 at 15:56

The only, and let me repeat THE ONLY data
is the total cumulative deaths resulting from it.

Even that is sketchy because many are untested,
and simply assumed to be caused by the current pandemic.

In short, we likely will never know the truth.

j_sum1 - 13-4-2020 at 16:15

 Quote: Originally posted by sodium_stearate THE ONLY data about this debacle that is not being cooked is the total cumulative deaths resulting from it.

I don't know that you can support that assertion. Certainly there is evidence that China is concealing the true situation. The same can be said for Turkmenistan and some other nations. As always, the full picture is limited by testing limitations.

But, at least where I am, the numbers seem to be a good representation. There are some troublesome clusters and leaky borders. But in general, the number of daily new cases is dwindling. There is some hope that we can ease restrictions soon and operate a test and isolate strategy. Reporting seems to be pretty good. Public understanding may be less so.

In any case, the OP is about modelling rather than data reporting.

[Edited on 14-4-2020 by j_sum1]

sodium_stearate - 13-4-2020 at 22:10

Understood. I will add that the best way to
analyze any model's faithfulness to reality is by
making a direct comparison of what the model predicts
versus what actually occurs.

The core issue here is that deaths are occurring.

Unless the cause of each death is properly tested,
there is no solid baseline to work from.

Accurate scientifically based modeling, working in
conjunction with thorough, scientifically based
testing is the only way forward here.

j_sum1 - 14-4-2020 at 00:14

I think we are on exactly the same page here SS. I would love to have the confidence of data that I knew was both compehensive and 100% accurate. But that is not the case for even idealised sampling never mind the sampling that occurs in situ in the middle of a crisis with scarce resources.

Here in Aus we appear to have passed over the bump. The number of reported new cases per day is the same as what it was exactly a month ago. And so people are (with some logic) saying that we have passed the worst and now it is time to ease up. What they don't appreciate is that exactly one month ago is when restrictions were put into place and we were experiencing exponential growth. If we revert too soon we could easily have exactly the same scenario that we had a month ago and we would have to brace ourselves for a second wave with a whole new round of deaths. That seems to be the situation that Singapore may be facing.

I do not think pandemic models are good for predicting outcomes. The situation is too volatile for that and there are a large number of unknowns when it comes to human behaviour. What models do well is predict the kind of patterns that can be expected and evaluate the probable effectiveness of various mitigation strategies. Clearly, if numbers are low enough, test and isolate combined with contact tracing and border control is likely to be the most effective as well as the least disruptive to day to day life. I would like to think that we will get to that stage soon, but realistically I think it may be another month minimum.

sodium_stearate - 14-4-2020 at 10:10

I personally think that the world's humans are
now in this scenario for the foreseeable future.
(In for the long haul)

As everyone else does, I too hope that it can

However, considering similar diseases such as
the flu and the common cold, this new and recent
virus is most likely here to stay as an added
menace to the long list of diseases.

That is a list of diseases which can be to some extent
mitigated. I predict some degree of mitigation, given
a sufficient amount of time and effort. Years perhaps.

SWIM - 14-4-2020 at 10:38

If it doesn't form new strains quickly like the flu it is very likely a vaccine that just needs being taken on a regular schedule will do the trick. Of course some cases will still happen, so they'll do quarantines like it's 1939.

We haven't had much in the way of casually communicable disease epidemics lately, but 80 years ago they'd lock everybody in the house and nobody gets out until the quarantine period is over. There was a city or county employee who'd come by and nail a sign up to warn people.

You don;t want to ignore that sign. If you go in, you stay.
If you're some unobservant delivery man who just walked in, well now you're a resident and not leaving until the health department says so.

This happened ALL THE TIME in the USA for things like measles, polio, etc.

It's how these things are handled, but we haven't had to all that often lately.

That may well change.

[Edited on 14-4-2020 by SWIM]

Twospoons - 14-4-2020 at 12:01

 Quote: Originally posted by SWIM If it doesn't form new strains quickly like the flu it is very likely a vaccine that just needs being taken on a regular schedule will do the trick. [Edited on 14-4-2020 by SWIM]

Well, looks like the first major mutation may have been found.
https://www.nzherald.co.nz/world/news/article.cfm?c_id=2&objectid=12324650

clearly_not_atara - 14-4-2020 at 13:09

 Quote: Originally posted by sodium_stearate In short, we likely will never know the truth.

What has been surprising to me about this pandemic is that regardless of political affiliation everyone is being so impatient. There will be many months, even years, after the pandemic when we will do retrospective analyses and try to find unreported cases/deaths, figure out what should/shouldn't have been done (in hindsight), and so forth. I think we will eventually get pretty close to the truth. The truth can't hide forever.

sodium_stearate - 14-4-2020 at 17:22

What I find most surprising is the fact that the last
big pandemic was in 1918.

That was 102 years ago.

Medical science is constantly crowing about how

To me, it does not seem to be nearly as advanced as
it claims to be.

j_sum1 - 14-4-2020 at 18:26

I think that medical advancements have come an awful long way. I have just had my pelvis bolted together and am expecting a fully recovery with no long term symptoms. My injuries 102 years ago would leave me lame, or more likely, dead.

Treatments have indeed come a long way. Pandemics are a public health issue and are not in the same category. Apart from a couple of scares, we really have not had much practice at dealing with this kind of thing. Mistakes have been made and are likely to continue. The post-pandemic learning and future-proofing will be critical.

Here is a list of some some significant advancements and also some particular hurdles that have had to be overcome. This may put things into perspective.
• Our world has become a lot more mobile than it was 100 years ago. This has made managing the pandemic a lot more complex.
• There has been, especially in the early stages, a lot of confusion and misinformation about the disease and the pandemic. There is no doubt that this has contributed to policy mistakes by governments. It has also contributed to people not fully understanding the situation and not taking it seriously or otherwise having a disproportionate response.
• This particular disease is a combination of high infection rate, low level symptoms for most and high mortality rate for those who are seriously affected. This combination is the worst possible for containing a pandemic.
• Mathematical modelling and simulation methods have never been better. They can inform public policy and facilitate good decision-making.
• Diagnostic tests are available in a way that was just not possible in 1918. Sure, we would like more, like them faster and like them more accurate. But the information they give has been extremely valuable especially for contact tracing. This was something that was just not possible 100 years ago.
• The ability to develop and test new treatments or modify existing treatments has never been better than it is now. The speed with which numerous organisations in the capitalist West have mobilised to create drugs and treatments is remarkable. The scale of this has not been seen before.
• Likewise there are good reasons to believe a vaccine will be developed in record time. Now, this might not eventaute. Coronaviruses are notoriously tricky. But there is optimism and a large number of people working on it. The science is well developed and, thanks to SARS, we are not needing to start from square one.
• We may wish to complain and there are variations across countries. But as a rule, the world economies are more robust and better resourced than was the case at the tail end of World War 1. Sure there is likely to be some repercussions, but the ability for many communities to bounce back is better than a century ago. The biggest concern here are high-density, low wealth nations such as Bangladesh and Indonesia which could potentially suffer serious impact without the resources to respond.

I hope this is a fair assessment. It is complex and there are multiple factors. But I don't think a lack of medical advancement is the key operative here.

arkoma - 15-4-2020 at 00:11

can't stop random code, ask Bill gates.
sodium_stearate - 15-4-2020 at 10:08

Certain types of medical science have advanced by a very significant amount during the past 102 years.

The way I see it, orthopedics is one of those categories

So, for bodies that have broken bones, cuts, lacerations,
wounds of many types, yes, the knowledge and technology
has advanced significantly during the past 102 years.

However, I do not see the same amount of advancement
in the area of prevention and/or mitigation of
infectious diseases. The way that looks to me is that civilization
is still pretty much in the dark ages.

Sigmatropic - 15-4-2020 at 10:27

Now for some actual models. https://science.sciencemag.org/content/early/2020/04/14/scie...

Haven't read the entire thing, yet, but it seems to me too much variables are unknown. That then gives you all these possible outcomes.

Edit: Discussion part is a gold mine in my mind. Let's hope for some favorable variables as I sure do not want to live in the world of fig 6a.

[Edited on 15-4-2020 by Sigmatropic]

clearly_not_atara - 15-4-2020 at 11:20

S_S: You don't consider the discovery of penicillin, sulfanilamide, streptomycin, chloramphenicol, isoniazid, chloroquine, nalidixate, dapsone, polymyxins, vancomycin, chlortetracycline, erythromycin, artemisinin, amantadine, miconazole, natamycin, oseltamivir, saquinavir and sofosbuvir to be "advancement in the area of mitigation of infectious diseases?"
karlosĀ³ - 15-4-2020 at 12:58

Lets not forget the golden antibiotic drug ceftriaxone, which is a drug I would even say that it saved my life from a spirochaete infection(don't mean syphilis)!
Medicine got really far from over hundred years ago, just not in each and every single issue, we just have started to battle virus infections properly and effective, but for everything else? Those things we have mostly very well under control.

sodium_stearate - 15-4-2020 at 15:56

Fair enough. I'll amend my previous statement
to read "We are still in the dark ages with viruses"

wg48temp9 - 12-5-2020 at 18:35

I built a pandemic simple growth model using Mathcad, using a reproduction parameter (R) an incubation duration parameter (time to become infectious), an infectious duration parameter and a recovery/death duration parameter. To make the model manageable those parameter were converted to rates per step of the model. That did not seem to work so I changed to two parameter a reproduction rate and a recovery/death parameter. ie a Susceptible-Infected-Recovered or removed (SIR) model. I got that to produce a bell like curve of the number of infected people. The cunve looked like the product of an exponential increase and an exponential decay to zero which suggested an analytical solution . I attempt to find the solution but failed. I did find paper with the analytical solution I am not surprised I could not find it. Attachment: pan-equations-1403.2160.pdf (219kB)