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SUMMARY:Space-time fractional diffusion equations in chemotaxis and immuno
 logy - Gissell Estrada-Rodriguez (Universitat Politècnica de Catalunya)
DTSTART:20231108T113000Z
DTEND:20231108T123000Z
UID:TALK203260@talks.cam.ac.uk
DESCRIPTION:In the presence of sparse attractants\, the movement of both c
 ells and large organisms has been shown to be governed by long distance ru
 ns\, according to an approximate L&acute\;evy distribution. In this talk w
 e clarify theform of biologically relevant PDE descriptions for such movem
 ents. Motivated by experiments we consider a microscopic velocity-jump mod
 el in which an individual performs occasional long jumps according to an a
 pproximate L&acute\;evy distribution. We derive the appropriate kinetic-tr
 ansport equation\, where the collision term describes the nonlocal motion.
  Under a perturbation argument and an appropriate parabolic scaling in spa
 ce and time\, we derive fractional Patlak-Keller-Segel equations [2].\nFur
 ther\, we consider the implications of such biological diffusion in the co
 ntext of T cell movement in the brain [3]. In response to Toxoplasma gondi
 i infections\, these cells have been shown to exhibit a mixed L&acute\;evy
  walk in which an additional resting time occurs between directional chang
 es. The resulting equation generates a time-fractional term and allows us 
 to formally interpret the results of [1]. Consequently\, we shed light on 
 the extent to which L&acute\;evy flight behaviour impacts on the average t
 ime taken for T cells to locate the sparsely distributed infected targets.
  We use the PDE description to present numerical results. This work is in 
 collaboration with H. Gimperlein\, K. Painter and J. Stocek.\nReferences[1
 ] T. Harris\, et al. Generalized L&acute\;evy walks and the role of chemok
 ines in migration of effector CD8+ T cells\, Nature 486\, 545&ndash\;548\,
  2012.[2] G. Estrada\, H. Gimperlein\, K.J. Painter. Fractional Patlak-Kel
 ler-Segel equations for chemotactic superdiffusion\, SIAP\, 78(2): 1155-11
 77\, 2018.[3] G. Estrada\, H. Gimperlein\, K.J. Painter\, J. Stocek. Space
 -time fractional diffusion in immune cell models with delay\, M3AS\, 29\, 
 65-88\, 2019.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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