Mathematics plays an essential role in epidemiology. Whether simple questions are asked about simple relations, or complicated questions about complicated relations, the best fitting mathematical figures are always searched for. In a holistic approach, it may often be necessary to assess complicated relations by using (real) mathematical models (simulation models). Examples are presented of parasitic contamination cycles which require more or less complicated mathematics to answer epidemiological questions regarding prevalence and incidence of infection in the human population: Trichinella, Toxocara and Toxoplasma. Some general remarks on epidemiological insights which are necessary to understand abstract concepts of the ‘real world’ (mathematical modelling), are discussed.