Seasonal impacts on brucellosis transmission mediated by live sheep supply-demand dynamics.

To explore how market supply-demand dynamics mediate seasonal brucellosis transmission, a non-autonomous periodic model with market feedback is developed, addressing the oversight of market-driven dynamics in existing models by integrating seasonal fluctuations of core market factors with epidemiological processes. Theoretically, coincidence degree and evolution operator theories confirm the existence and global asymptotic stability of periodic solutions in the market-disease framework, achieving methodological and socio-epidemiological modeling innovations. Validated with Xinjiang's 2018-2022 brucellosis surveillance data, numerical simulations show seasonal fluctuations in livestock off-take rates and breeding recruitment potential drive the disease's periodic transmission, revealing a unique market-mediated pathway independent of biological and climatic factors. A key insight is that disease detection efficiency critically depends on the market-culling competition ratio with temporal heterogeneity, challenging the universal optimality of stricter detection and highlighting market mechanisms' non-negligible role. Policy analysis finds strengthening environmental disinfection is more feasible and cost-effective for regional control than only improving detection/culling rates. The model also identifies a bidirectional feedback loop: epidemic policies reshape livestock supply and market prices, while price signals regulate farmers' herd management via profit incentives, further modulating transmission risk. In conclusion, effective brucellosis control requires synergizing epidemiological interventions and market management, with dynamic, differentiated cross-sectoral strategies accounting for both epidemiological and market drivers.