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Barrier Function Model

Conceptual framework describing physical barriers (gloves, masks, drapes) that prevent the transfer of microorganisms between contaminated and sterile zones.
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The statement of the theorem

Consider a boundary ∂Ω\partial \Omega separating a contaminated zone ΩC\Omega_C and a sterile zone ΩS\Omega_S. The transfer rate of microorganisms, JJ, across this boundary is modeled by a flux equation: J=−D∇C⋅n∣∇C∣+ktransfer(CC−CS)J = -D \nabla C \cdot \frac{\mathbf{n}}{|\nabla C|} + k_{transfer} (C_{C} - C_{S}) where CC is the microbial concentration, DD is the diffusion coefficient, n\mathbf{n} is the normal vector, and ktransferk_{transfer} is the rate constant representing physical barrier efficacy. The barrier function requires ktransfer→0k_{transfer} \rightarrow 0 for effective separation.