A dynamical model of tumour immunotherapy

Mathematical Biosciences
Federico FrascoliKerry A Landman


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 is also shown that the tumour shape, characterised by a surface area to volume scaling factor, influences the size of the basin, with significant consequences for therapy design. The findings reveal that the tumour volume must surpass a threshold size that depends on lymphocyte parameters for the cancer to be completely eliminated. A semi-analytic procedure to calculate oscillation periods and determine their sensitivity to model parameters is also presented. Numerical results show that the period of oscillations exhibits notable nonlinear ...Continue Reading


Dec 10, 2015·Current Problems in Cancer·Rachel Walker, Heiko Enderling
Jan 16, 2020·Journal of the Royal Society, Interface·Prativa SahooRussell C Rockne


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MBNL1 gene
Tumor Cells, Uncertain Whether Benign or Malignant
Immune Response
Immune System
Abnormal Degeneration
TC2 Cells
Rostrotemporal Auditory Area
Lymphocytes as Percentage of Blood Leukocytes (Lab Test)

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