An epidemiological model of African cassava mosaic virus disease (ACMD) was developed in which the dynamics within a locality, of healthy and infected cassava, and of infective and non-infective whitefly vectors, were specified. Cassava is propagated routinely from stem cuttings. If the exclusive use of virus-free cuttings was assumed then either a high rate of virus transmission by the vector or a large population of vectors could lead to persistent cycles in disease incidence. Such cycling could seriously impair cassava production. When frequency-dependent use of infected cuttings was admitted, however, persistent cycles of infection were no longer possible. Instead, three states could occur: disease eliminated (E), both healthy and diseased cassava persisted (P), or infection became total (T). The outcome depended on the particular parameter values, but some parameter combinations gave state P or T, depending on the initial conditions. In some instances, low initial incidence of ACMD posed a greater risk of progressing to state T than did higher levels of infection. In general, disease incidence exhibited a discontinuous, threshold response to changes in the proportion of infected cuttings used. An increase in their use could appear to have little impact on incidence, although the system was moving closer to a point of sudden increase in infection. Simulation of the removal (roguing) of diseased plants had little influence on disease incidence, but had an important and largely cryptic effect by helping to move the system away from the threshold of collapse of the healthy cassava population. Intensification of cassava production (represented in the model as an increase in the maximum possible abundance of cassava) had the opposite effect, moving the system closer to this threshold. Assuming a degree of disease ‘reversion’, whereby a proportion of the cuttings derived from infected plants are uninfected, had a stabilising influence on the model, making even damped cycles of disease very unlikely. Total infection did not now occur except at very low reversion rates. The response of disease incidence to the increased use of infected cuttings was no longer discontinuous but remained non-linear and there was a region of rapid change corresponding to the threshold seen in the absence of reversion.