Archive for SEIR model

Ireland’s Covid-19 Models

Posted in Covid-19, mathematics, Maynooth with tags , , , , , on July 1, 2021 by telescoper

Yesterday the Chair of the National Public Health Emergency Team (NPHET), who also happens to be the President of Maynooth University, Professor Philip Nolan published a lengthy but interesting Twitter thread (which you can find unrolled here). In these tweets he explained the reason behind NPHET’s recommendation to pause the process of relaxing Covid-19 restrictions, postponing the next phase which was due to begin on 5th July with indoor dining.

The basic reason for this is obvious. When restrictions were lifted last summer the reproduction number increased to a value in the range 1.4 to 1.6 but the infection rate was then just a handful per day (on July 1st 2020 the number of new cases reported was 6). Now the figures are orders of magnitude higher (yesterday saw 452 new cases). A period of exponential growth starting from such a high base would be catastrophic. It was bad enough last year starting from much lower levels and the Delta variant currently in circulation is more transmissable. Vaccination obviously helps, but only about 40% of the Irish population is fully immunized.

Incidentally the target earlier this year was that 82% of the adult population should have received one jab. We are missing detailed numbers because of the recent ransomware attack on the HSE system, but it is clear that number has been missed by a considerable margin. The correct figure is more like 67%. Moreover, one dose does not provide adequate protection against the Delta variant so we’re really not in a good position this summer. In fact I think there’s a strong possibility that we’ll be starting the 2021/22 academic year in worse shape than we did last year.

In general think the Government’s decision was entirely reasonable, though it obviously didn’t go down well with the hospitality sector and others. What does not seem reasonable to me is the suggestion that restaurants should be open for indoor dining only for people who are fully vaccinated. This would not only be very difficult to police, but also ignores the fact that the vast majority of people serving food in such environments would not be vaccinated and are therefore at high risk.

As things stand, I think it highly unlikely that campuses will be open in September. Rapidly growing pockets of Delta variant have already been seeded in Ireland (and elsewhere in Europe). It seems much more likely to me that September will see us yet again in a hard lockdown with all teaching online.

But the main reason for writing this post is that the thread I mentioned above includes a link to a paper on the arXiv (by Gleeson et al.) that describes the model used to describe the pandemic here in Ireland. Here is the abstract:

We describe the population-based SEIR (susceptible, exposed, infected, removed) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g., to the daily number of confirmed new cases, as the past history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data, to produce a robust methodology for calibration of a wide class of models of this type.

You can download a PDF of the paper here.

This model is a more complicated variation of the standard compartment-based models described here. Here’s a schematic of the structure:

This model that makes a number of simplifying assumptions but it does capture the main features of the growth of the pandemic reasonably well.

Coincidentally I set a Computational Physics project this year that involved developing a Python code that does numerical solutions of this model. It’s not physics of course, but the network of equations is similar to what you mind find in physical systems – it’s basically just a set of coupled ODEs- and I thought it would be interesting because it was topical. The main point is that if you study Theoretical Physics you can apply the knowledge and skills you obtain in a huge range of fields and disciplines. Developing the model does of course require domain-specific epidemiological knowledge but the general task of modelling complex time-evolving systems is definitely something physicists should be adept at doing. Transferable skills is the name of the game!

P.S. It came as no surprise to learn that the first author of the modelling paper, Prof. James Gleeson of the University of Limerick, has an MSc in Mathematical Physics.