title: Model for acid-mediated tumour invasion with chemotherapy intervention II: Spatially heterogeneous populations.
abstract: 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.
authors.affiliation: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia. Electronic address: abh920@uowmail.edu.au.
authors.forename: Andrew B
authors.initials: AB
authors.lastname: Holder
authors.affiliation: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia. Electronic address: marianito_rodrigo@uow.edu.au.
authors.forename: Marianito R
authors.initials: MR
authors.lastname: Rodrigo
mesh_terms: D000143:Acids / Q000378:metabolism; D003198:Computer Simulation; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D009369:Neoplasms / Q000188:drug therapy* / Q000378:metabolism / Q000473:pathology*
chemical_list: D000143:Acids
keywords: Chemotherapy; Periodic functions; Reaction-diffusion system; Travelling wave; Warburg effect