Abstract
Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (ASN) (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against ASNs and control strategies largely rely on crop rotation to nonhost crops or by planting resistant varieties of alfalfa. In this paper, we present a basic host-parasite model that describes the spread of the ASN on alfalfa crops. With this discrete time model, we are able to portray a relationship between the length of crop rotation periods and the time at which the density of nematode-infested plants becomes larger than that of nematode-free ones in the postrotation alfalfa. The numerical results obtained are consistent with farming practice observations, suggesting that the model could play a role in the evaluation of management strategies.
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