Bull Math Biol (2014) 76:401–430 DOI 10.1007/s11538-013-9925-3

© The Author(s) 2013. This article is published with open access at Springerlink.com Abstract Dose and time intensifications of chemotherapy improved the outcome of lymphoma therapy. However, recent study results show that too intense therapies can result in inferior tumour control. We hypothesise that the immune system plays a key role in controlling residual tumour cells after treatment. More intense therapies result in a stronger depletion of immune cells allowing an early re-growth of the tumour. We propose a differential equations model of the dynamics and interactions of tumour and immune cells under chemotherapy. Major model features are an expo-nential tumour growth, a modulation of the production of effector cells by the pres-ence of the tumour (immunogenicity), and mutual destruction of tumour and immune cells. Chemotherapy causes damage to both, immune and tumour cells. Growth rate, chemosensitivity, immunogenicity, and initial size of the tumour are assumed to be patient-specific, resulting in heterogeneity regarding therapy outcome. Maximum-entropy distributions of these parameters were estimated on the basis of clinical sur-vival data. The resulting model can explain the outcome of five different chemother-apeutic regimens and corresponding hazard-ratios. We conclude that our model explains observed paradox effects in lymphoma ther-apy by the simple assumption of a relevant anti-tumour effect of the immune system