Plant nematodes belong to a large group of invertebrates known as round worms, They derive their name from the Greek word "nema," meaning thread. In literature some authors refer to nematodes as nemas. In England and many parts of the United States, plant-parasitic nematodes are called eelworms. While some damage to plants results from mechanical injury, salivary secretions injected by the nematode into the plant are usually the major cause of damage. Experiments conducted in the first part of the present century have demonstrated large differences in plant growth in soil infested with nematodes and soil freed of nematodes by chemicals. Any plant subjected to nematode attack is reduced in growth. The most important nematode which attacks and retards the growth of alfalfa in Utah is the stem nematode. This parasite has been reported in most of the major alfalfa-producing counties of the state. In certain areas the nematode is prevalent to such a degree that only resistant varieties can be grown if the crop is to remain for more than two or three years. In other areas stands and yields are reduced in varying degrees. In many additional areas it is not known if the stem nematode is present, since a complete survey of the state has never been made. The objectives of this investigation were to determine the distribution of the stem nematode of alfalfa through a complete survey of the state. The physical factors of the plant and soil which may be correlated with the presence of the nematode were likewise surveyed.

Alfalfa is a major cash crop in the western United States, where fields that are infested with the alfalfa stem nematode (Ditylenchus dipsaci) can be found. With no nematicides available to control alfalfa stem nematode spread, growers can use nematode resistant varieties of alfalfa to manage nematode populations in a field. A deterministic, discrete-time, host-parasite model is presented that describes the spread of alfalfa stem nematodes on resistant hosts that was fit to experimental data obtained in Weber County, Utah. Numerical results obtained from simulations with the model are used to compare how varying levels of resistance can affect harvest yield. Resistant varieties can also affect the invasion speeds of epidemics in crops. A continuous time, spatial model is presented that describes how these resistant varieties affect invasion speeds in general crop systems. Speeds of traveling wave fronts are determined for simple epidemics in crops that contain a mixture of resistant and non-resistant hosts. For the model, it was found that the wave speeds will slow down as highly nematode resistant varieties of alfalfa are used. The speed of invasion for the alfalfa stem nematode can be determined by using a mathematical relationship that is know as the contact distribution. We present a spatial model for the spread of alfalfa stem nematodes that uses a Gaussian distribution as the contact distribution of the alfalfa stem nematodes, which was determined by experimental data. Using this contact distribution we are able to approximate the speed of nematode invasive fronts in absence of advection, i.e. without nematode trans-port through flood irrigation. The contact distribution is then used to calculate front speeds when resistant varieties of alfalfa are introduced. We found that, unsurprisingly, invasive speeds are relatively low and cannot support the rapid dispersal of the disease among fields as seen in practice. However, this result leads to conjecture that changing current irrigation practices, from flood to sprinkle irrigation, could effectively contribute to control the spread of alfalfa stem nematodes. Resistant varieties of alfalfa can be used to effectively control the spread of the alfalfa stem nematode. In this work we have shown that using resistant varieties of alfalfa can increase yield up to 83%, they can slow down invasion speeds of nematodes, and switching from flood to sprinkler irrigation could effectively contribute to the control of the alfalfa stem nematode.