Great point ... chemotherapeutics work on "rapidly dividing cells" (cancer cells, hair, cuticles, skin, intestinal tract, etc.) faster than slowly dividing cells ... parasites might just be included in that "rapidly dividing cell" category also.
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... Another interesting thought is the chemo regimens they use to fight these cancers are often based on drugs which are toxic to rapidly growing cells such as cancer, but also affecting hair and GI tract cells and probably parasites as well.