Final answer:
Smallpox caused the most deaths among Amerindians in the 15th and 16th centuries. The Spanish Flu was the pandemic spreading at the end of the war. The development of the smallpox vaccine was a major medical innovation of the late 19th century.
Step-by-step explanation:
Regarding the student's question, smallpox was responsible for the greatest number of deaths among Amerindian populations in the late fifteenth and early sixteenth centuries. In contrast, at the end of the war mentioned in the student's question, it was the influenza pandemic, often referred to as the Spanish Flu, that spread around the world. These diseases were extremely contagious and often spread through close contact between individuals or via contaminated objects and surfaces.
An important medical innovation of the late nineteenth century related to combating such diseases was the development of the smallpox vaccine, which was a significant breakthrough in preventing one of the deadliest diseases known to humanity at that time.