Sunday, 17 July 2011

Dawn of the Dead

Given my age, I was a young teenager when videos arrived in the UK, and horror movies were the rage. I'm pretty sure that the first zombie movie I saw was Dawn of the Dead (the original, although the recent remake wasn't that bad).

Dawn is one in a long line of zombie films by George A. Romero, colloquially known as the Living Dead Series, starting with the classic Night of the Living Dead in 1968. Some of the later movies are, well, not so good, but Dawn is an excellent movie (well, excellent zombie movie).

I'm not going to give the story away here, but as noted in Dawn (and especially the recent Zombieland), there will be survivors, and these survivors will get better at surviving by not being killed, and getting rid of more zombies. As noted in Zombieland;
The first rule of Zombieland: Cardio. When the zombie outbreak first hit, the first to go, for obvious reasons... were the fatties
 So, in my zombie models, I have added a factor to account for the "hardening" of the population, by making the various parameters a function of time. As a reminder, here's the starting point, with all the parameters kept constant.

I've modified the plot and now, on the bottom, have the key parameters that control the zombie apocalypse. These are α, humans killed by zombies, β, humans infected by zombies, and δ, zombies killed by humans.

With the constant values given above, the population crashes.

OK, let's change these. What I've done is use a logistic function to change the values. The key points to this is a time which represents the mid-point of the change, a time scale and a size of change. Here's one where the population stiffens at around 300 days.

Again, the population collapses and the zombies take over. What we need to do is make the population stiffen a lot earlier. Let's get the population fighting back harder at about 250 days, during the collapse of the population.

Now this is more like it. What we see now is that the population drops, but the stiffening of the population halts the decline and the population flattens out and the zombies are basically eradicated.

Moving the stiffening back again, we should expect the population to do better, and to go back to 200 days, we find
So the rule is simple. Fight back, and the earlier we fight back, the better.

Keep your eyes peeled for the shuffling undead!

3 comments:

  1. Why is the number of dead so much larger, comparatively to the number of Zombies? What function are you using to determine the number of conversions from infection?

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  2. Ahh never mind sorry, I see there are earlier posts :) Shall read some more! Great fun stuff! well done!

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  3. Hi Dropbear - Long time etc etc. I'm glad someone is reading my posts :)

    Yes, take a look at the previous posts. I'm sure my zombie model isn't perfect. If you have any thoughts, I'm happy to give them a whirl. The infection period comes next.

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