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Agricultural losses to pests represent an important challenge in a global warming scenario. Intercropping is an alternative farming practice that promotes pest control without the use of chemical pesticides. Here, we develop a mathematical model to study epidemic spreading and control in intercropped agricultural fields as a sustainable pest management tool for agriculture. The model combines the movement of aphids transmitting a virus in an agricultural field, the spatial distribution of plants in the intercropped field and the presence of 'trap crops' in an epidemiological susceptible-infected- removed model. Using this model, we study several intercropping arrangements without and with trap crops and find a new intercropping arrangement that may improve significantly pest management in agricultural fields with respect to the commonly used intercrop systems. [ABSTRACT FROM AUTHOR]