Model for acid-mediated tumour invasion with chemotherapy intervention II: Spatially heterogeneous populations

•We model the acid-mediation hypothesis with the inclusion of a cytotoxic treatment.•The model examines constant and periodic treatment protocols.•Constant and periodic treatment exhibit analogous overall behaviour.•Treatment reduces the impact of acid and slows the speed of tumour invasion.

This paper extends the model for acid-mediated tumour invasion with chemotherapy intervention examined in part I. The model presented in part I considers the interaction between tumour cells, normal cells, acid and drug in a well mixed (i.e. spatially homogeneous) setting, which is governed by a system of nonlinear differential equations. The model examined here removes the assumption that the populations are spatially homogeneous resulting in a system of nonlinear partial differential equations. Numerical simulations of this model are presented for different treatment methods displaying several possible behaviours. Asymptotic approximations are also derived for a special case of the treatment method and set of parameter values. This analysis then allows us to draw conclusions about the effectiveness of treating acid-mediated tumours with chemotherapy.