For this case we can translate the sentence given as:
The __________________ of the indigenous people increased due to the different diseases that the Spaniards brought to the region.
We know that with the arrival of the Spaniards to the American continent, the death rate of the natives increased due to the large number of diseases that the Spaniards brought.
The main ones were smallpox and measles.
Then, we can complete the sentence as:
The mortality rate of the indigenous people increased due to the different diseases that the Spaniards brought to the region.
Answer:
La tasa de mortalidad de los indígenas aumentó por las distintas enfermedades que trajeron los españoles a la región.