Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics


Luis Gordillo


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 (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow end-users to design better management programs and farming practices. This is of particular importance given that there are no nematicides available against alfalfa stem nematode and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties. I present a basic host-parasite model that describes the spread of the alfalfa stem nematode on alfalfa crops. With this discrete time model I am 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 healthy ones in the post-rotation 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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