Introduction

Please note: While I did study mathematical epidemiology a long time ago, I am not an epidemiologist and your national government has access to much better data and models to track and predict the spread of the virus and risks associated to it. The aim of this site is to illustrate that some, hopefully, relatively easy to understand mathematics can be used to explain how the virus spreads through the population, and how certain actions can slow/stop it.

But before I start there are a number of items which I don't believe have been addressed very well in the media, and have resulting in reduced trust in science being reduced, namely:

• Mathematical Modelling
• and R₀, the basic reproduction number.

Anyone who just wants to skip straight to the model and project what might happen/might have happened with their own country can just click below.

Go to final COVID-19 model

"The only models I've heard of are the likes of Naomi Campbell".

I've heard the above a lot over the years, and it's just not true. Model cars, trains, airplanes architectural models of buildings (even dolls' houses), are examples of models that the vast majority of people will have heard of, if not seen or interacted with. They are simplifications of the real objects, but still give us a sense of what is going on. Likewise mathematical models involve simplifying what is going on. The building of mathematical models often requires no maths at all, the maths is only used at end to get answers. This is the case with the modelling of infectious diseases such as COVID-19.

R₀, aka R-zero, aka R-nought, aka the basic reproduction number. This terminology should never have made it into the public domain without a reasonable discussion of the latent period [time from being infected to being infectious], duration of infectiousness [i.e. how long a person is infectious] and serial interval [average time between one person showing symptoms and the next person in the chain showing them (roughly equally to latent period plus half the duration of infectiousness)].

"The radio said R nought was three, then one, now zero point seven, meaning every person who has the virus now gives it to point seven of a person. What's point seven of a person? Do you not either have it or not."

Here's my attempt at an explanation, for R₀ equal to 3, 1 and 0.7, and an average infectiousness duration of 7 days and latent period of 2 days and a serial interval of 5.5 days, with 1000 infections at the start.

• For R₀ equal to 3:
• After 7 days the initial 1000 are no longer infectious but they've passed it on to 3000 (typically by 5.5 days, so there's an overlap), who will in turn pass it on to 9000 ... 13000 already have had it.
• If the disease has a high chance of causing serious illness the healthcare system will be quickly overrun.
• For R₀ equal to 1:
• After 7 days the initial 1000 are no longer infectious but they've passed it on to 1000, who will in turn pass it on to 1000 ... 3000 already have had it.
• This may sound manageable but just because your not infectious doesn't mean you don't need hospitalisation for longer than 7 days.
• For R₀ equal to 0.7:
• After 7 days the initial 1000 are no longer infectious but they've passed it on to 700, who will in turn pass it on to 490 ...
• This is more like it.

I believe the timescales really matter to the general public as it can give some measurable degree of hope. In reality the range of serial interval could be from 2 days to 11 days, hence the 14 day quarantine.

R₀ is directly related to the number of close contacts an infected person has. As we roll back keeping this as low as possible is crucial to avoid needing future lockdowns.