We present a mathematical model which is used to interpret the dynamics of the immunological response of a mouse host to infection with the filarial worm Onchocerca lienalis. The model mimics changes in worm burden over time post-infection and after reinfection and its behaviour provides a good description of experimental results. Measured production of T-cells and eosinophils is also compared with the predictions of the model. Our results show that the immune response mechanism proposed on the basis of experimental results, involving CD4+ T-cells and eosinophil destruction of the parasite, is supported by the insights gained from the mathematical model. Also, using the parameters estimated to describe the primary infection dynamics, the degree of acquired immunity to secondary infection is also well described by the model. Our analysis highlights the importance of obtaining quantitative measures of the many rate parameters involved in even the simplest interpretations of immunological responses to parasitic infection.