The way that parasites grow and spread is closely related to their respective life cycle. Even though there are some notable exceptions, such as the very rare but life-threatening free-living amoebae, pathogenic parasites are usually obligate parasites requiring infecting one or many hosts in order to fulfill successfully their life cycle. The parasites then undergo several differentiation stages within their respective host(s). Intermediate hosts are usually required for the maturation stages of the parasites or to facilitate spreading to the final host, for instance when the intermediate host is an insect-vector. Then, adult or mature form of the parasite is present in the final hosts that are used by the parasite to survive and reproduce. It is interesting to note that resources from the hosts, such as nutrients, is taking by the parasite to survive, grow and reproduce in order to fulfill successfully its life cycle. As such, the growth including the different changes between the various forms of the parasite is closely related to its specific hosts.
Some protozoan parasites species (but not all) are also able to persist in harsh conditions in a cystic form. This cyst is considered as a dormant stage, which is able to survive for quite a long period of time in a toxic environment, without food or without the proper temperature favourable for their growth. When the cyst encounters a favourable environment again, it will develop back in its parasitic form. The subsequent parasitic stages are also linked closely to their intermediate hosts and to their modes of transmission. For example, some protozoan parasites such as Leishmania, Trypanosoma and Plasmodium are transmitted by an insect-vector that acts as an intermediate host. The form of the parasite within the insect-vector is then different than the one in the final human host. However, in that case, only the parasitic form that is present within the insect-vector is able to infect successfully human.
One the other hand, helminths begins their life cycle in the form of eggs that latter transform into larvae. Infection of the intermediate and/or the final host is usually made by contact or ingestion of eggs or larvae. The larvae have also a quite complex maturation cycle that may involve many stages within their host(s) depending on the species involved before the transformation into their mature form. Mature adult worms are usually present within their final host.
Finally, spreading of the different parasites is closely related to their specific modes of transmission.
Source: Centers for Disease Control and Prevention