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An Age and Spatially Structured Model of Tumor Invasion with Haptotaxis II

Author

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  • JANET DYSON
  • ROSANNA VILLELLA-BRESSAN
  • GLENN WEBB

Abstract

An analysis of a model of tumor growth into surrounding tissue is continued from an earlier treatment, in which the global existence of unique solutions to the model was established. The model consists of a system of nonlinear partial differential equations for the population densities of tumor cells, extracellular matrix macromolecules, oxygen concentration, and extracellular matrix degradative enzyme concentration. The spatial growth of the tumor involves the directed movement of tumor cells toward the extracellular matrix through haptotaxis. Cell age is used to track progression of cells through the cell cycle. Regularity, positivity, and global bounds of the solutions of the model are proved.

Suggested Citation

  • Janet Dyson & Rosanna Villella-Bressan & Glenn Webb, 2008. "An Age and Spatially Structured Model of Tumor Invasion with Haptotaxis II," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(2), pages 73-95.
    • Handle: RePEc:taf:mpopst:v:15:y:2008:i:2:p:73-95
    DOI: 10.1080/08898480802010159
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    Cited by:

    1. Urszula Foryś & Jan Poleszczuk & Ting Liu, 2014. "Logistic Tumor Growth with Delay and Impulsive Treatment," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(3), pages 146-158, September.

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