Maedi-visna (MV) is a complex lentiviral disease syndrome characterised by long immunological and clinical latencies and chronic progressive inflammatory pathology. Incurable at the individual level, it is widespread in most sheep-keeping countries, and is a cause of lost production and poor animal welfare. Culling seropositive animals is the main means of control, but it might be possible to manage virus transmission effectively if its epidemiology was better quantified. We derive a mathematical epidemiological model of the temporal distributions of seroconversion probabilities and estimate susceptibility, transmission rate and latencies in three serological datasets. We demonstrate the existence of epidemiological latency, which has not explicitly been recognised in the SRLV literaure. This time delay between infection and infectiousness apparently exceeds the delay between infection and seroconversion. Poor body condition was associated with more rapid seroconversion, but not with a higher probability of infection. We estimate transmission rates amongst housed sheep to be at about 1,000 times faster than when sheep were at grass, when transmission was negligible. Maternal transmission has only a small role in transmission, because lambs from infected ewes have a low probability of being infected directly by them, and only a small proportion of lambs need be retained to maintain flock size. Our results show that MV is overwhelmingly a disease of housing, where sheep are kept in close proximity. Prevalence of MV is likely to double each year from an initial low incidence in housed flocks penned in typically-sized groups of sheep (c. 50) for even a few days per year. Ewes kept entirely at grass are unlikely to experience transmission frequently enough for MV to persist, and pre-existing infection should die out as older ewes are replaced, thereby essentially curing the flock.