How do blood cells fight disease?

White blood cells fight disease; there are several types of white blood cell, but all come under the umbrella term of 'leukocytes'. Each type of leukocyte works on a different threat, or in a different way, but one type chemically poisons bacteria to kill them, & another type wraps itself around a bacteria & carries it away in the bloodstream.

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Sorry to disagree, but not all white blood cells are leukocytes. Leukocytes are B-cell, T-cell, and Natural Killer cells which are involved in acquired immunity (you develop it after being born).

Macrophages, mast cells, neutrophils, oesinophils, and basophils are phagocytes (innate immunity-you are born with them), which engulf the pathogen and either kill it right away or signal to leukocytes that a pathogen is present (antigen presenting cells).