Disease Spreading Problem


by Swimmingly!
Tags: disease, spreading
Swimmingly!
Swimmingly! is offline
#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.
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism

Register to reply

Related Discussions
What is spreading resistance? Electrical Engineering 1
Spinor spreading Quantum Physics 3
The spreading stain Special & General Relativity 13
Spreading wavepackets Quantum Physics 3
Light Spreading General Physics 16