How a Pandemic Works - And What Stops It?

The General Case

To answer this question, I've created a simulation where an infectious disease is transmitted via a grid of interacting cells to see if I'm able to codify my experience through mathematical modelling. Click on any blue cells below to artificially infect them before clicking "Run Simulation".

You've just witnessed a "nearest neighours" infection model. When you click "Run Simulation" above, an infected cell (red) in the bottom right corner can spread through a population through its "nearest neighbours". Infected cells, if adjacent to healthy cells (blue), have a certain moderate probability (p) of transmitting the disease to them. Each infected cell has a chance of recovery (r, grey recovered cells), and of course, re-infection is possible. The keen observer would have observed that I've left out three events:

• We could have coded for death, perhaps a black cell to indicate this. (Think about what implications this would have on your system!)
• I've neglected long range interactions (e.g. when someone travels between places).
• I've assumed the chance of recovery is constant with infection.

As expected, the steady-state distribution is about 50:50 between infected and recovered, defaulting to the chance of recovery. But note the rapid transmission of the disease through nearest-neighbour infection. No healthy cells are left, and this gives you some sense of what living with the disease means - it's not that no one gets the disease, but we reach some sort of manageable equilibrium.

Speed & Extent of Transmission

What governs the extent and speed of transmission? Let's see what happens when we run the same simulation for three cases of "low", "moderate" and "high" transmission probability - more specifically, let's also tweak the ratio between p and r (I've pre-infected one cell in these simulations):

Depending on low the ratio is, you could end up with a disease transmission that self-terminates. I suppose that is somewhat like the common flu, where we've learnt to recover somewhat quickly enough relative to the speed of transmission. On the flip side, you could also have a disease that rages out of control if the ratio is too high - recovery is too slow to bring down the infection numbers.

Breaking the Transmission

Is it possible to model the effect of vaccination or social distancing? Many ways actually! One way would be to code some vaccinated or socially distanced cells as inert (green cells), so that they do not become nodes of transmission. Let's run the simulation again, this time with 0% and 10% of such isolated cells that are essentially non-interacting:

Could we extend this to a more extensive model? Possible! Suppose you divided the map of Singapore into discrete blocks, where each block is composed of such an interacting array of cells. Each block has a baseline transmission probability, intrinsic to the disease. But depending on the human traffic and risk of imports (e.g. airport or checkpoint regions), you assign higher probability tiers accordingly. You could then allow for long-range interactions in addition to nearest-neighbour interactions to simulate the effect of human movement.

Essentially, you've just created a policy sandbox to investigate the effects of your public health policy interventions. Cool beans!

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