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Chain of Infection Interruption

The core public health principle applied in surgery: breaking the chain (Infectious Agent →\rightarrow Reservoir →\rightarrow Exit →\rightarrow Mode →\rightarrow Portal →\rightarrow Susceptible Host) to prevent transmission.
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The statement of the theorem

Model the chain of infection as a directed graph G=(V,E)G = (V, E), where VV is the set of nodes (Reservoir, Exit, Mode, Portal, Susceptible Host) and EE is the set of directed edges representing transmission pathways. Interruption is achieved by introducing a set of interventions I≜{i1,i2,…,ik}I \triangleq \{i_1, i_2, \dots, i_k\} such that the resulting graph G′=(V,E\Einterrupted)G' = (V, E \backslash E_{interrupted}) contains no directed path from the initial pathogen source to the susceptible host. Mathematically, this requires Path(Vsource→Vhost)=∅\text{Path}(V_{source} \rightarrow V_{host}) = \emptyset in G′G'.