Building models V: Epilogue

In part I of this blog series, I tried to explain the ideas behind doing the whole modelling exercise, the maths of the SIR model and fictional virus, Divoc-91; in part II I started to use the published data on covid-19 to get some sensible numbers (or starting parameters) for my model; in part III I put the spreadsheet together; in part IV, I worked out what the model actually told me, and so here, in part V (which might be the last one for a while), I’m trying to work out what my conclusions are.

So what….?

First of all I’m glad I managed to do the modelling. It’s not really that hard once you have the ‘basic mechanism’ for what your doing. Having looked at some of the papers that are around, I wonder how much original work is being done by virus modellers right now, and how much is changing the parameters in existing modelling programs. However, even then the models had to be built originally, so the work ‘had’ to have been done at some point.

Ro values are both critical and irrelevant. Unless you can get the Ro value less than a certain value (in this Divoc-91 model the value was 2.5) nothing really matters, the mortality is extreme (1 to 1.3 million Divoc-91 dead) and it’s all over within the year. Once it gets below 2.5 there’s all to play for, and you get massive returns every time you lower Ro by 0.1 or 0.2. For Divoc-91, there seemed to be a sweet spot at Ro=1.5 where the spread of the virus peaks at about 2 years, 60% of the community catches the virus (and so there’s some level of herd immunity), and the health services are not overwhelmed.

The other advantage of a low Ro value is that it delays the spread of the virus and gives the scientists a chance to develop a vaccine. You need to vaccinate at or, even better, before the peak of the virus, for it to have any real effect on mortality. While for Divoc-91 Ro at 1.5 seemed to be a sweet number for a vaccine to be delivered at 18 months, extrapolating these results to Covid-19, where we’re being told that we’ll be lucky to have a vaccine within 18 months, this means that any extra time we can get before the peak is valuable: 1.3 is better than 1.4, which is better than 1.5.

This SIR/Excel model (unlike the real modelling done by the proper modellers at Imperial College, London School of Tropical Medicine and may other research institutes) can’t tell us how to get to low Ro values. Personally, I think it’ll be tracking and tracing via mobile phones, social/physical distancing, and a moratorium on large gatherings for up to 2 years (may be more).

Therapeutic and pharmaceutical interventions

For Divoc-91, the big benefits seemed to be in finding some medical treatment, or drug therapy, that reduces the number of people needing intensive care. Increasing the number of ICU beds, or improving patient outcomes once they got into ICU didn’t overcome the issue of saturating ICU at the peak of the disease.

Problems with the model

I have a theoretical issue with part of the model. The equation that tells me how many people move from the infected to the recovered group (here) is a first order rate equation. While the SIR model uses that equation, it basically says that if I take 100 people and immediate infect them, one day later five of them will have moved to the recovery group, and the for next three days after that (days 2-5) another five will move to the recovery group, and then for the next five days (days 10-15) after that, four will move to the recovery group and so one. But it doesn’t work that way in reality, where none of the 100 newly infected patients would move into the recovery group (say for example) for 10 days, then the number of people moving per day would increase until day 20, when it would gradually fall back to zero.

Possibilities of the model

The problem above could be solved by changing the equation which tells me how many people move from the infected to the recovered group to one which looks back 20 days and moves the same number of people (as 20 days ago) rom the infected to the recovered group.

The model could also be altered to move a certain proportion of infected people to the recovery group (say 90%) and the rest (in this case 10%) back to the susceptible group. This might mimic the situation of immunity to Divoc-91 wasn’t universal.

Final shoutout

I was pretty much inspired to try some modelling after looking at some cool modelling stuff from the maths youtuber 3Blue1Brown. His great modelling system (which are far more sophisticated than this one) that he just plays with trying different ideas is below.

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