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| This talk addresses a coupled chemotaxis-haptotaxis system modeling cancer cell invasion of surrounding tissue, which describes the interplays between the cancer cell density, the concentration of a matrix-degrading enzyme (MDE) and the density of extracellular matrix (ECM). In addition to random movement, cancer cells are supposed to bias their movement both towards increasing concentrations of urokinase plasminogen activator by chemotaxis, and towards increasing densities of the non-diffusible ECM through detecting the macromolecules adhered therein by haptotaxis. It is assumed that the cancer cells undergo birth and death in a logistic manner, competing for space with the ECM. The MDE is assumed to be produced by cancer cells, and to diffuse and decay, whereas the ECM is assumed to be degraded upon contact with MDE. We will discuss the global existence, boundedness and asymptotic behavior of solutions to the system, which strongly depend on the model parameters and initial conditions. |
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