Covid-19 model scenarios for UK

Social distancing slows down the spread of Covid-19 by reducing the reproduction factor $R_0$ . If $R_0$ is reduced below 1,  then the number of cases and deaths will begin to fall, but how effective is this strategy long term and how can we escape from a lockdown once it has been  imposed. I have looked a bit into this using my “Mickey Mouse” SIR model. Interestingly enough it gives similar results to that of Neil Fergusen if I use the same parameters (R=2.5 etc).

First here is the simulation for the UK under the “take it on the chin” scenario.

“Take it on the chin”. The epidemic is over after ~ 3 months but at the cost of half a million deaths !

These results assume a death rate of 1% and an effective $R_0$ of 2.5. Half a million deaths is unacceptable for any government which probably explains why the lockdown measures were introduced, once the Imperial study was published. The goal of a lockdown is to reduce the reproduction rate $R_0$ to below 1 by decreasing the contact rate $\beta$ (social interaction) by about 70%. Once successful this lockdown would then result in the following distribution assuming the measures are introduced after ~40 days into the epidemic (mid March) and ended after 100 days.

Effects of a 3 month long lockdown followed by a return to near normal

It takes about 3 months for the lockdown to reduce the number of active infections to a low level (<10%). However once the restrictions are lifted the epidemic quickly takes off again, which then triggers another full lockdown. If such action is taken quick enough then the epidemic can finally be stopped as shown below.

Stop-Go scenario: A lockdown and release followed by a second lockdown a month later.

This last scenario seems finally to work in reducing the infected cases to a very low level. However the final number of deaths is still large ~92000. The damage to the UK economy of a 3 month shutdown followed by a second emergency shorter shutdown would be  enormous. Could the UK ever recover from such an economic shock and would  the UK public be willing to accept such a 7 month period of drastic stop-go action ?

These scenarios may be far too pessimistic. Two recent studies of antibodies in sample populations seem to show that the infection rate (15%) is currently much higher than thought, and consequently that the death rate could be as low as 0.3% (see my comment below & here). That would reduce the predicted death tolls by a factor of 3.  Furthermore one would hope that more effective treatments will be found to reduce the death rate even further. An effective vaccine would eliminate the risk completely.

My raw python code can be found here

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12 Responses to Covid-19 model scenarios for UK

1. Andrew Carey says:

Does your code allow for R0 changing over time : initially the biggest most mobile most social people spreading the virus are most likely to get it and would presumably be excluded from spreading it again.

• Clive Best says:

Yes it is easy to change that over time. In fact that is all I essentially do for lockdowns by changing beta – the social interaction parameter with time. I should probably tidy up the code and make all parameters configurable in a file. Right now I just hack the code.

2. Bryce F Payne says:

Clive, you state,
“Two recent studies of antibodies in sample populations seem to show that the infection rate (15%) is currently much higher than thought…”
Which studies were those?

• Clive Best says:

The first was a German study in Gangelt which was heavily effected with Covid-19. 14% of 500 randomly sampled people were antibody positive which implied and infection to mortality rate -> 0.37%.

See here

The second was in the town of Robbio, Lombardia which likewise found an infection rate of 14%. My guess is that the same percentage might now apply to London, most of whom were asymptotic.

• Hello Clive, the random testing suggests infection rates of between 10 and 15%. I can’t see how 0.1% of UK population could infect half the Scottish care homes. It must be that that the virus is more visible there.

• Clive Best says:

Hi Iain,

You probably only need one infectious care worker per care home to eventually infect all the residents. So if you have say 70 residents who meet up daily in a communal lounge with 50 staff (cooks, cleaners, helpers, nurses etc), then I think it probably is likely that half care homes get infected with Covid-19 even at a 10% rate.

• ok to infect 50% of care homes you would need 0.7% of 70 care workers to be infected.

3. Robert Johnson-Taylor says:

The trouble with all these models they are too narrowly focused. It is necessary to consider the deaths caused by enforced lock down; families forced to remain in close proximity for protracted periods of time, not only result in assults, but also murders and suicides. The elderly living alone without adequate, if any support, resulting in death by neglect. The mentally ill not capable of being left to support them selfes. The UK government is allready building up body recovery resources for post lockdown, and are being told this is going to be very unpleasent. But the real killer, the biggest killer of all is poverty. Employment that once existed will have gone, together with their markets. This economic reality will be inter-generational

• Clive Best says:

You are absolutely right. The long term effects of any extended lockdown are huge and unknown. Perhaps governments have over-reacted – even Trump has been forced into a lockdown against his instincts. I can’t see any way out of this unless we can first find an effective treatment to cut deaths, and later develop a vaccine. Until humans build an immunity to the virus through vaccine or disease we can only suppress infections in the short term, but as you say at huge social and economic costs.

• Robert Johnson-Taylor says:

I have seen posts, from reputable sources, that there is a growing body of evidence that COVID19 is a man made virus. no I’m not a conspiracy theorist. The Chinese government produced it, and it escaped, not a deliberate act.

4. Clive Best says:

Hong Kong closed the borders early and has an efficient testing, tracking and quarantine program. The first case occurred on 23 January and since then there have been as of today (13th April) only 1004 cases with just 4 deaths. This implies a death rate of 0.4%

If this applies globally then for the UK the above estimates would give

“Take it on the chin” : 230,000 deaths
“Stop Go” : 48000 deaths but still a small number (140) left infected risking a further increase.

5. mesocyclone says:

A strategy that a lot of countries are going for is to use the strong social distancing to knock the number of cases down to a level where traditional means – testing, and contact tracing with individual quarantine – can be used after that, with a lot less social distancing. Then… keep the levels low until a vaccine is available. In that strategy, Rt is kept lower than R0 by some distancing, but mostly by containing any outbreak before the numbers get too big.

That could not be used at first because too much was unknown, plus it takes time to scale up testing and contact tracing logistics.

BTW, I’m not an epidemic modeler, but my reading suggests that Rt (short for R(t)) is used for the reproduction number that diverges in time (for whatever reason) from R0.