Joint work with Claudia Neuhauser, U. of Wisconsin

Coexistence in Some Competition Models

This project began as an attempt to understand the competition of different strains of the barley yellow dwarf, specifically the following graph which gives the prevalence of the MAV and PAV strains in a study Rochow (1979) conducted near Ithaca.

With this aim we developed a model in which each site in the two dimensional integer lattice can be in state 0 = healthy, 1,2 = infected by that strain, 3 = infected by both. In words, new 1 infections occur at rate b1 times the fraction of infected neighbors (for your favorite neighborhood) but (a) doubly infected neighbors count for c1 < 1, and (b) infections into a 2 infected site occur at c1 times the rate for an uninfected site. As in the contact process, a plant that is 1 infected becomes healthy at rate d1, but here, doubly infected plants lose their 1 infection at rate d1/c1. There are of course, constants b2, c2, d2 and analogous transitions for 2 infections. Our basic question is: Can the two strains coexist? The picture below of the nearest neighbor system with b1=2, d1=1, b2=3, d2=1, c1 = c2 = shows that the answer is yes.

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