The human lung is constantly exposed to spores of the environmental mould Aspergillus fumigatus, a major opportunistic pathogen. The spectrum of resultant disease is the outcome of complex host-pathogen interactions, an integrated, quantitative understanding of which lies beyond the ethical and technical reach permitted by animal studies. Here we construct a mathematical model of spore inhalation and clearance by concerted actions of macrophages and neutrophils, and use it to derive a mechanistic understanding of pathogen clearance by the healthy, immunocompetent host. In particular, we investigated the impact of inoculum size upon outcomes of single-dose fungal exposure by simulated titrations of inoculation dose, from 106 to 102 spores. Simulated low-dose (102) spore exposure, an everyday occurrence for humans, revealed a counter-intuitive prediction of fungal persistence (>3 days). The model predictions were reflected in the short-term dynamics of experimental murine exposure to fungal spores, thereby highlighting the potential of mathematical modelling for studying relevant behaviours in experimental models of fungal disease. Our model suggests that infectious outcomes can be highly dependent upon short-term dynamics of fungal exposure, which may govern occurrence of cyclic or persistent subclinical fungal colonisation of the lung following low dose spore inhalation in non-neutropenic hosts.