Recent experiments reveal targeted therapy of tumours promotes the spread of drug-resistant cancer cells in mixed sensitive-resistant tumours. The hypothesis is that drug-stressed sensitive cells produce diffusible growth factors that stimulate the expansion of drug-resistant cells. A mathematical model employing simple ecological competition and a nonlinear motility law is able to reproduce the magnitude of observed expansion of the resistant populations volume without invoking production of diffusible growth factors. The model shows how the therapy-induced removal of the sensitive population alleviates the competitive pressure on the resistant for resources and space and confirms the in vivo experimental findings, and sheds light onto mechanisms behind the large increase of the drug-resistant cancer cells in the treated tumour.
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