What causes the sickness among the slaves that
equiano describes in this passage?

The overcrowded conditions and bad air lead people to become sick.

Explanation:

This is the passage for this question:

The closeness of the place, and the heat of the climate, added to the number in the ship, which was so crowded that each had scarcely room to turn himself, almost suffocated us. . . . [T]he air soon became unfit for respiration from a variety of loathsome smells, and brought on a sickness amongst the slaves, of which many died. . . . The shrieks of the women, and the groans of the dying, rendered the whole scene of horror almost inconceivable.

Explanation of passage:

Just from the first sentence we can see that there was many people in a cramped space that was extremely hot and when someone gets hot that also means that they are going to be sweaty. From this we can infer that people got sick due to the overcrowded conditions and bad air because an area that is damp, hot, and crowded is a perfect place for disease/sickness to breed.

they remained in rural areas and worked at jobs such as lumbering or farming.