Connecting a Chemotactic Model for Mass Attack to a Rapid Integro-Difference Emulation Strategy

We present an approach to emulating a complicated reaction/chemotaxis/diffusion model describing the spatial dispersal of mountain pine beetles (MPB) and their effect on host pines. The approach depends on separation of scales between chemical diffusion and beetle movement, which reduces the dispersal problem to a linear PDE with complicated, spatially varying coefficients. We develop an approximation procedure for solving this linear system in general circumstances and analyze its errors. Finally, we analyze the behavior of the system, using the previous procedure to take extremely large numerical time steps. We show that the qualitative dynamics are preserved even when the pointwise error may be large, which leads us to propose this approach as a general emulation technique for similar systems.

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