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I'm interested in obtaining some measure of contact (or encounter) likelihood between two individuals, each is spatially distributed with some probability density function at time ##t## such that,

Space use of individual 1 = ##u(\mathbf{x}, t)##

Space use of individual 2 = ##v(\mathbf{x}, t)##

Would I solve for the area overlap between ##u(\mathbf{x},t)## and ##v(\mathbf{x},t)##, perhaps by taking the integral of their joint distribution? Or should I take the convolution of the two? Frankly, I'm not sure when convolution method is actually applicable. Furthermore, once I have the contact rates at time ##t## across the entire domain, to find its value within a certain region (say, ##a \leq x \leq b## in 1D domain), do I simply take the integral of the resultant contact PDF from ##a## to ##b##?

Sorry if this question is too elementary. I really appreciate all your help!!

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# Contact rate between individuals of different probability density functions

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