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The role of tumor-stromal interactions in progression is generally well accepted, but their role in initiation or treatment is less well understood. It is now generally agreed that, rather than consisting solely of malignant cells, tumors consist of a complex dynamic mixture of cancer cells, host fibroblasts, endothelial cells and immune cells that interact… (More)

We consider the steady state of an open biochemical pathway, with controlled flow. Previously we have shown that the steady state of open enzyme catalysed reactions may be unstable, which discourages the application of the quasi-steady-state approximation (QSSA) [IEE Proc.-Syst. Biol. 153 (2006) 187]. Here we examine basic open biochemical pathway… (More)

There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution. We consider the case where both solution types may be… (More)

Convection-induced instability in reaction-diffusion systems produces complicated patterns of oscillations behind propagating wavefronts. We transform the system twice: into lambda-omega form, then into polar variables. We find analytical estimates for the wavefront speed which we confirm numerically. Our previous work examined a simpler system [E. H.… (More)

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