You can find the answer to this question by reading in Chapter 11. The answer is given most clearly and concisely on pages 212 and 213 in the paperback edition. This is close to the end of the chapter.
There, Diamond tells us that New World diseases were less virulent because of geographical luck. He says that serious epidemic diseases come from large populations of people who have contact with one another and also with large numbers of animals. These conditions existed in the Old World but not in the new. In the New World, there were no domesticated herd animals that lived in close contact with people. There were also few large groups of people and those who did exist were not in contact with one another. In these ways, the New World lacked animals to give diseases to people and the human populations needed to become a "breeding ground for microbes (p. 212)."