Towards a theory of insect epidemiology

Summary An attempt is made to consolidate and extend some of our current thoughts on insect epidemiology using graphical reproduction models. Starting with a simple model with a single equilibrium point, the elementary hypothesis is proposed that epidemics erupt when this equilibrium point increases substantially through improvement of the insect's habitat. The extension of this model to more than one coincident equilibria, some of which may be locally stable, is discussed and generalized using the theory of habitat suitability. Use of equilibrium manifolds is suggested to permit greater dimensionality. Lastly, an explanation of insect epidemics, based on the effects of time delays in the response of density-dependent processes, is elaborated and generalized. The influence of spatial dimensions and insect dispersal on the theory is discussed. Scientific Paper No. 4890, College of Agriculture Research Center, Washington State University. Modified from a paper presented at the joint meeting of the Sociedad Mexicana de Entomologia and the Pacific and Southwestern Branches of the Entomological Society of America, held at Guadalajara, Mexico, April 17–22, 1977. This work was conducted under Project 102 and was supported by the State of Washington and the National Science Foundation (Grant Nos. GB-30752 and GB-34718).