Mathematical analysis of a tumour-immune interaction model: A moving boundary problem

Abstract

Studies indicate that some people have lived with a non-cancerous tumour for theirВ entire life. This is attributed to the interactions between the host immune system withВ tumour cells. Nonetheless, the specific biochemical and cellular mechanisms by whichВ immune cells manage to keep tumour cells dormant are still not clearly understood. InВ this paper we develop and analyse a spatio-temporal mathematical model, in the formВ of a moving boundary problem, in a bid to explain cancer dormancy. Analysis of the
model is carried out for both temporal and spatio-temporal cases. Stability analysis andВ numerical simulations of the temporal model replicates experimental observations ofВ immune-induced tumour dormancy. Travelling wave solutions of the spatio-temporalВ model are determined using the hyperbolic tangent method. A stability analysis of theВ spatio-temporal model showed a possibility of dynamical stabilization of the tumour-
free steady state. Simulation results reveal that the tumour radius first increases but afterВ sometime reduces to a dormant level. Our approach may lead to a deeper understandingВ of cancer dormancy and this may be helpful in the future development of better andВ effective therapeutic methods.