Math Biology Seminar: Chad Topaz

In this mathematical modeling talk, we discuss two projects on socially aggregating insects. The first project models desert locusts with an eye towards hopper band aggregations. Via analysis and simulation of a nonlinear partial integrodifferential equation model, we find conditions for the formation of population density clumps, demonstrate transiently traveling pulses of insects, and discover hysteresis in the aggregation's existence. The second project uses motion tracking experiments on the pea aphid to construct a random walk model for their motion. The random walk parameters depend strongly on distance to an aphid’s nearest neighbor. For large nearest neighbor distances, when an aphid is isolated, its motion is ballistic and it is less likely to stop. For short nearest neighbor distances, an aphid moves diffusively and is more likely to become stationary; this behavior constitutes a simple aggregation mechanism.