You can answer this question by reading in Chapter 11. Diamond gives the answer on pages 204 and 205 in the paperback edition of the book.
The answer is that these diseases are slow to develop. The fact that they are slow to develop means that they do not kill their hosts quickly. Because their hosts continue to live, they continue to provide habitat for the germs. If the germs acted like the epidemic diseases, they would simply wipe out their host populations. Epidemic diseases can only survive in huge populations of people. Early in human history, huge populations did not exist. This meant that the earliest diseases had to spread slowly. Therefore, the disease you mention in this question had to be the earliest human diseases.