The SEIR Model

The Next Wave

Suppose that we assume the data from Wuhan. Now, suppose that social distancing is relaxed beginning at 120 days. A gradual lifting of mitigation occurs between 120 days and 240 days, so that at 240 days, Rzero is now 1.75. As we shall see, this causes a second wave of infection, so that once again, social distancing is imposed, at day 240, with Rzero returning to 0.5 at day 360. The second wave actually peaks higher than the first wave. This assumes that the beginning of the next wave is recognized early, but the reintroduction of social distancing takes longer the second time around (i.e. more people need to keep working). [PHOTO]

All Models are Wrong, Some are Useful

This is a quote from the statistican George Box. There has been much criticism in recent days about model predictions, and the widely varying forecasts for the number of coronavirus cases. As you can see from the above, small changes in the R_zero input have a large effect on the output. With no social mitigation efforts, this number is already hard to determine. Now, you also have to determine how social distancing and quarantines effects R_zero, and how fast this occurs. You should try different scenarios for R_zero yourself, to get a feel for how difficult it will be to make reliable forecasts.

But, as Box points out, it is useful to play around with these models, since it gives you an understanding of the factors at play.

Research Question

The SEIR model assumes a "well mixed" homogeneous population. This is obviously not true over a large geographic region. One way to extend this model is to assume that (S,E,I,R) are spatially distributed. Then, the quantities which appear on the rhs of the ODE system are spatially smoothed. This will give rise to a system of Partial Integro-Differential Equations (PIDEs). See Archiv paper arXiv:1909.01330. Another approach is to use a network based SEIR model, i.e. nodes in the network represent different populations. Contacts between the populations occur through a network See Archiv paper arXiv:2006.06939. In addition, there is a large amount of randomness associated with disease spread, so a better model uses stochastic differential equations to simulate pandemics.

The GLEAM model includes both spatial and stochastic effects.

Webinar April 29, 2020 at 2:30pm (GMT+1)

Mathematics of the COVID19 crisis – In the eye of the storm