# Zombie PDE model

1. Nov 20, 2009

### Lionheart814

Hey guys,

I'm currently taking a Partial Differential Equations class, and for one assignment we have to come up with a model for a theoretical zombie outbreak. Well anyways, this is what I have gathered thus far:

- I am defining my u(r,z,t) to be the population density of humans, where r=radius, z=zombies, and t=time.
- There will be a continuous flow in and out of humans out of the boundary.
- I am letting my boundary be a circular region, suppose a 35 meter radius.
- The population density of both zombies and humans is dependent on the radius, r, of the region. For example if you have 100 zombies in a particular radius with 50 humans, if you increase the radius then the population density decreases.

I think I may have my boundary condition where Du/Dr(35,z,t)= flux, since the normal derivative will always be the radius.

My Initial condition is u(r,z,0)= u0

Now, the PDE is where I am having trouble, I can't figure out what Du/Dt is (the rate of change of human population density with respect to time).I tried modeling it similar to the heat equation, but that doesn't work since I only have one spatial dimension in r, and no theta. As r changes as does the total density (zombies and humans) and therefore human density.

If no one knows how to do it this way, then how about in terms of polar coordinates with theta?

Last edited: Nov 20, 2009
2. Nov 21, 2009

### HallsofIvy

Staff Emeritus
The Laplacian in polar coordinates is
$$\nabla^2 f= \frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial f}{\partial r}\right)+ \frac{1}{r^2}\frac{\partial^2 f}{\partial \theta^2}$$

If f is circularly symmetric (independent of $\theta$), this is just
$$\nabla^2 f= \frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial f}{\partial r}\right)$$

3. Nov 21, 2009

### redxakma88

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:shy:

Last edited by a moderator: Apr 24, 2017
4. Nov 21, 2009

### Lionheart814

I'm sorry, but that is of little help THawk and Red. I do not know who this Laval person is, and I would appreciate that you cease your trolling at once, or face certain consequences by a moderator.

Thank you.

5. Nov 21, 2009

### redxakma88

mr lionheart
we're gona send this link to dr. lav

gl~

and i hope this formula helps~

Last edited by a moderator: Apr 24, 2017
6. Nov 22, 2009

### HallsofIvy

Staff Emeritus
So you are all in the same class? I'm glad I'm not teaching that class. (And so should you be.)