What if?

It's a while since I did any real forecasting, the current system just runs on a bit into the future with the R values gradually spreading out due to the daily random perturbations, and the end result is pretty obvious. Now with the effective R value probably just above 1, and various further relaxation planned (e.g. end of furlough, schools returning) jules thought it would be interesting to see what might possibly happen if R goes up a bit.

Here are two ensembles of simulations, both tuned the same way to historical data, which gives an R_effective of about 1.1 right now. The step up on the 4th July is a modelling choice I made through choice of prior, in allowing a large change on that one day only rather than a gradual ramping up around that time. In the first set of forecasts, I ramp up R by 0.5 over 30 days through September. For the modellers, I'm actually using R as my underlying parameter, calculating R_effective based on the proportion of people who (it is assumed!) have acquired immunity through prior infection. So typically the underlying R value is going up from 1.2 to 1.7 or thereabouts. You can see the resulting ramp up in R_eff on the plot, with the subsequent drop entirely due to the herd immunity factor kicking in as the second wave peaks. The new peak in deaths is...not pretty. I'm disappointed it is so severe, in my head I'd been assuming that a much lower R number (compared to the 3-3.5 at the start) and non-negligible level of current immunity would have helped to keep it lower.

The second set of results is a more optimistic assumption where R only goes up by 0.2, this time in a single step when the schools go back near the start of Sept (don't quote me on the date, it was just a guess). However....it's still not great I'm afraid. The lower R gives a more spread out peak and there is a chance of things turning out not too badly but a lot of the trajectories still go up pretty high, with most of them exceeding the April max in daily deaths, and sustaining this for quite a while.

So...that's all a bit of a shame. There are however reasons why this may be a bit too pessimistic: it is well-known that this simple model will overestimate the total penetration of the disease as it doesn't account for heterogeneity in the population, which could make a significant difference. Also, I've kept the fatality rate at 0.75% despite advances in treatment which have definitely nudged it lower than it was at the start. On the other hand, the model does not account for loss of immunity here among people who have had the virus. Not clear if that simplification is truly valid over this time scale.

Anyway, these are not predictions, I just put in some reasonable-sounding (to me!) numbers to see what would happen. It does look like any further significant increase in R will have serious consequences.