Live bird markets (LBMs) act as a network 'hub' and potential reservoir of infection for domestic poultry. They may therefore be responsible for sustaining H5N1 highly pathogenic avian influenza (HPAI) virus circulation within the poultry sector, and thus a suitable target for implementing control strategies. We developed a stochastic transmission model to understand how market functioning impacts on the transmission dynamics. We then investigated the potential for rest days-periods during which markets are emptied and disinfected-to modulate the dynamics of H5N1 HPAI within the poultry sector using a stochastic meta-population model. Our results suggest that under plausible parameter scenarios, HPAI H5N1 could be sustained silently within LBMs with the time spent by poultry in markets and the frequency of introduction of new susceptible birds' dominant factors determining sustained silent spread. Compared with interventions applied in farms (i.e. stamping out, vaccination), our model shows that frequent rest days are an effective means to reduce HPAI transmission. Furthermore, our model predicts that full market closure would be only slightly more effective than rest days to reduce transmission. Strategies applied within markets could thus help to control transmission of the disease.