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• Constructed an operation architecture of the coupling of energy supply and demand. • Established the comprehensive demand response mechanism based on time-sharing energy prices. • Established the minimum carbon emission cost economic scheduling model as an objective function. • The scheduling method could achieve the goal of low-carbon economic dispatch. Aiming at the problems of low energy utilization and environmental pollution in China's livestock and poultry breeding industry under the carbon peaking and carbon neutralization goals, this paper proposes an optimal scheduling model for multi-energy coupling integrated energy system with ladder-type carbon trading mechanism and demand response. First, based on the construction of a reward and punishment model with ladder-type carbon trading mechanism, this paper explores the potential interaction between the coupling ability of multiple heterogeneous energy sources and carbon emissions in consideration of the impact of carbon capture equipment on carbon emissions. Second, in view of the diversity and complexity of demands for agricultural energy supply, the energy supply side equipment model and the comprehensive demand response model of electricity, heat, and gas are established, and a low-carbon economic scheduling model of integrated agricultural energy system is proposed, aiming at minimizing the total operation cost of the system. Finally, the model is solved by CPLEX, and the coupling system of a 6-node power distribution network, a 6-node gas network, and a 4-node heat supply network is used to verify the effectiveness of the proposed model and method and optimize the operation of the integrated agricultural energy system. [ABSTRACT FROM AUTHOR]