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.