Aerosol bolus dispersion has attracted attention due to its value in non-invasive clinical diagnosis of lung function and also due to its influence on particle deposition in the pulmonary region of the lung. The two salient observations from bolus dispersion experiments are that (1) dispersion increases linearly with inhaled volume and (2) dispersion is higher in a diseased lung than a healthy one for similar volume penetration. A number of plausible causes for dispersion have been proposed and discussed in the literature. However, a clear physical mechanism responsible for dispersion is still not available. Using a simple hypothesis for convective mixing, we propose an approximate physically based model to quantify bolus dispersion in the human airways. We then develop a computational model to simulate dispersion in the human lung and compare the model predictions to experimental data. This simple model, employing no adjustable parameters, predicts many observations of bolus dispersion.