That depends entirely on the parasite.
Some have a life cycle that requires two hosts. Generally those are transmitted by food items. For instance, a snake eats a frog (intermediate host) that is infected with the larval stage of a parasite. These larvae then grow to adulthood, then reproduce in the snake (final or definitive host). Eggs, oocysts, or larvae are then deposited into the environment (usually through feces) and are then picked up again by an intermediate host. This is what is known as an Indirect Life Cycle. Normally these types of parasites are self-limiting when there is no intermediate host available.
Others have a Direct Life Cycle. These are capable of reproducing, then reinfecting the definitive host without an intermediate host. In captivity, when clean conditions are not maintained, these are capable of building up overwhelming populations in the host.