Comparison of two mathematical models for the Echinococcus multilocularis-red foxes-rodents interactions

Abstract

The paper sets up two mathematical models for the Echinococcus multilocularis’s life cycle in the environment. Herbivores are the intermediate hosts, harboring its larval stage, while carnivores host the adults. From the wild this helminth can spill to domestic animals and thus it could be potentially harmful for humans. The models differ in the way disese transmission is modeled. Feasibility and stability of the systems’ equilibria are assessed. No persistent oscillations can arise. The study of the transcritical bifurcations between the steady states provides maps that are useful for the applied ecologist for possible parasite eradication.