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Cestodes are parasitic flatworms, of the phylum Plathelminthes, which tipically live in the digestive tract of adult vertebrates (definite hosts) and frequently parasite other species of animals in the early stages of their developments (intermediate hosts). One possible example of this system is the interaction between different species of helminthes that parasite ungulates in North America in their early development. The ungulates are the main resource in wolfs' diet in this region and, upon predation, the juvenile parasites infect the wolfs, their definite hosts, completing the parasites' cycle.

However, wolfs can also predate alternative prey, like beavers, which are not intermediate hosts to many wolf parasites. A recent study (Friesen and Roth, 2016) has shown that alternative resources use is correlated with reduced incidence of parasites in wolfs. This suggest that alternative resources use by wolfs might have an important influence on the parasite prevalence on the community, what can be beneficial both for wolfs and ungulates.

Propose a simple mathematical model to study the prevalence of parasites in the system composed by wolfs and two possible prey (e.g. ungulates and beavers). You may as well start with wolfs and ungulates and study the infection dynamics on the populations, and only then introduce an alternative prey and see how this balance is altered.

Here are some questions you may explore, but further well-grounded insights are also welcome.

• Friesen, O.C. and Roth, J.D., 2016. Alternative prey use affects helminth parasite infections in grey wolves. Journal of Animal Ecology.