In this article, we develop a mathematical model for the spreading of the wool-bearing sheep in a population of herders in the Near East and Southeast Europe between 6200 and 4200 BC. Herders are considered as agents moving diffusively in a suitability landscape, such that motion into regions attractive for sheep herding are more probable than to unattractive regions. Simultaneously agents interact socially with another and pass on the innovation with some probability. The parameters of the agent-based model are fitted to available archaeological information. A simulation tool is proposed for computing the evolution of the spreading process in time and space, offering a way to study qualitative effects of different aspects affecting speed and spatial evolution of the spreading process.