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Disease Spreading Problem

by Swimmingly!
Tags: disease, spreading
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Swimmingly!
#1
Sep26-13, 05:12 AM
P: 45
I came up with an ill-defined problem that I'm not sure on how to approach:
We have XR^2 space and I(X){0,1}. If I(X)=1 X is infected, if I(X)=0 it's not.
The probability of an X_0 infecting X is proportional to e^(-(X-X_0)^2). If at t=0 the circle X^2<1 is infected what's the average looking I(X,t)?
What kind of maths deals with these problems?

Rigor: An obvious way to approach this is a discrete way. Instead of XR^2 use N^2. And instead of tR use tN and decrease the size of dt and dX. The weird part is N^2 is not isotropical like R^2 is.
To give rigor to proportional to e^(-(X-X_0)^2), I could say that the time derivative of density in infected cells is proportional to the integral of e^(-(X-X_0)^2) or something of the sorts.
I'll keep it short and just wait or suggestions.
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