Uniqueness of limit cycles in models for microparasitic and macroparasitic diseases.

The aim of this paper is to prove the uniqueness of isolated periodic solutions (i.e. limit cycles) in two simple models for microparasitic and macroparasitic diseases. Both models are described by systems of planar autonomous ordinary differential equations. After transformation of these systems to generalized Liénard systems, we will apply a modified theorem of Zhang and Dulac's criterion to prove the uniqueness of limit cycles.