The answer is infection. Milady's own definition matches the question almost word for word: "infection..., which is the invasion of body tissues by disease-causing pathogens." This is the foundational vocabulary term the rest of the Sanitation chapter builds on — sterilization, disinfection, and sanitizing are all described in relation to preventing infection.
Disinfection, contamination, and fission — the other choices — are related but distinct terms: disinfection is the process of killing pathogens (the fix), while infection is the invasion itself (the problem). Fission is unrelated cell-division terminology, not an infection-control term at all.
Milady Standard Barbering, 6th ed., Ch. 4 (Infection Control), p. 62: "infection..., which is the invasion of body tissues by disease-causing pathogens."
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