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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5134-5146. doi: 10.3934/mbe.2020277
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Global boundedness and stability for a chemotaxis model of Boló’s concentric sclerosis

  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received: 27 June 2020 Accepted: 20 July 2020 Published: 31 July 2020

  • Baló's concentric sclerosis (BCS) is considered a variant of inflammatory demyelinating disease closely related to multiple sclerosis characterized by a discrete concentrically layered lesion in the cerebal white matter. Khonsari and Calvez (Plos ONE. 2(2007)) proposed a parabolic-elliptic-ODE chemotaxis model for BCS which describes the evolution of the densities of activated macrophages, cytokine and apoptotic oligodendrocytes. Because "classically activated" M1 microglia can produce cytotoxicity, we introduce a linear production term from the activated microglia in the ODE for pro-inflammatory cytotoxic. For the new BCS chemotaxis model, we first investigate the uniform boundedness and global existence of classical solutions, and then get a range of the chemosensitive rate χ where the unique positive equilibrium point is exponentially asymptotically stable.

    Citation: Xiaoli Hu, Shengmao Fu. Global boundedness and stability for a chemotaxis model of Boló’s concentric sclerosis[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5134-5146. doi: 10.3934/mbe.2020277

    Related Papers:

  • Baló's concentric sclerosis (BCS) is considered a variant of inflammatory demyelinating disease closely related to multiple sclerosis characterized by a discrete concentrically layered lesion in the cerebal white matter. Khonsari and Calvez (Plos ONE. 2(2007)) proposed a parabolic-elliptic-ODE chemotaxis model for BCS which describes the evolution of the densities of activated macrophages, cytokine and apoptotic oligodendrocytes. Because "classically activated" M1 microglia can produce cytotoxicity, we introduce a linear production term from the activated microglia in the ODE for pro-inflammatory cytotoxic. For the new BCS chemotaxis model, we first investigate the uniform boundedness and global existence of classical solutions, and then get a range of the chemosensitive rate χ where the unique positive equilibrium point is exponentially asymptotically stable.


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