Humour me in showing how restricting movement can #flattenthecurve of an epidemic using some models (my aim is no more nor less than this - I claim no groundbreaking science here - see end of thread).

Consider a population that lives on a square grid. Contacts can be 'global' (random with anyone else on the grid) or 'local' (just your 4 near-neighbours). Everyone is either Susceptible, Infected or Recovered and only processes are infection and recovery.

I will show results from 3 types of model:
* 10x randomised (stochastic) simulations - blue lines
* The classic SIR math. model (that does not include space) - black line
* An approximate math. model (that includes a bit of space) - red line
R0=2.5.

First, assume everyone's contacts are completely global. This is actually just the classic SIR model. All 3 models show a peak incidence of 25% infected, and after 6 months 89% of population has caught it.

Now assume complete movement restriction so everyone's contacts are entirely local. This shows huge flattening of curve. Peak is down to <5%. By day 180 <50% of population have caught it, and it can even have died out.

Animating the dynamics shows why this happens (ht to @Natasha1777 for getting these working nicely!). Because infection is neighbour-to-neighbour it often blocks itself and cannot spread to new Susceptibles easily.

Extremes are always unrealistic. How restrictive do we need to be to control infection? Would half local-half global be enough? Not really - peak is still around 20% and we still end with 85% having caught it.

Again, an animation highlights why. Even with 50% of contacts local, there are enough global contacts to allow infection to jump to new region and seed a new local epidemic.

If you want to halve peak of epidemic, you actually need >85% of contacts to be local.

The point of all this? Restricting movement can dramatically flatten the curve of an epidemic, but the restrictions need to be really quite strong.

Code (with further info) on my webpages: http://abest.staff.shef.ac.uk/teaching.html  To be clear: this is just a model with many assumptions (see code). I am not claiming major insight for covid-19 at all; just trying to demonstrate an interesting model.