A dynamical model of tumour immunotherapy
Federico Frascoli, Peter S Kim, Barry D Hughes, Kerry A Landman
MATHEMATICAL BIOSCIENCES | ELSEVIER SCIENCE INC | Published : 2014
A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillations, or unbounded solutions. To investigate the dependence of the dynamic behaviour on model parameters, the equations are solved analytically and conditions for unbounded versus bounded solutions are discussed. An analytic characterisation of the basin of attraction for oscillatory orbits is given. It..View full abstract
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The work of PSK was supported by an ARC Discovery Early Career Research Award. The work of FF, BDH and KAL was supported by an ARC Discovery Project. The authors thank an anonymous reviewer for the constructive and stimulating comments, which helped to improve the quality of this paper significantly.