Final answer:
Without treatment, African sleeping sickness invariably leads to death due to brain and nervous system damage caused by Trypanosoma brucei, the parasite responsible for the disease.
Step-by-step explanation:
Without treatment, African sleeping sickness invariably leads to death due to brain and nervous system damage. Trypanosoma brucei, the parasite responsible for African sleeping sickness, changes its surface glycoproteins with each infectious cycle, evading the immune system. The immune response against the parasite is unable to clear it, allowing it to continuously replicate and spread throughout the body, affecting the central nervous system. This damage to the brain and nervous system ultimately leads to death.