Phenotypic plasticity and competition shape therapy sequencing in HER2⁺/HER2^- breast cancer: A mathematical framework

Tumour heterogeneity and phenotypic plasticity are major drivers of treatment failure in cancer, enabling rapid adaptation under therapeutic pressure. In HER2-positive (HER2⁺) breast cancer, tumours often contain both HER2⁺ and HER2-negative (HER2^-) cells whose interactions complicate schedule design. We develop a compact ordinary differential equation framework for intratumoral HER2⁺/^- dynamics that integrates phenotypic plasticity with density-dependent growth and inter-phenotype competition. Phenotype-specific therapies are incorporated through simple pharmacodynamic surrogates: Paclitaxel chemotherapy acting primarily on HER2⁺ cells and Notch-pathway inhibition targeting HER2^- cells. We use the model to compare staggered and simultaneous treatment schedules. The results show that treatment order and relative intensity critically shape long-term tumour composition. Targeted-first schedules can exhibit competitive release, whereby subsequent aggressive chemotherapy unintentionally favours HER2^- expansion. In contrast, simultaneous initiation suppresses both phenotypes more effectively and avoids strong rebound. These findings highlight the importance of ecological structure in therapy design and support simultaneous combination therapy followed by targeted maintenance.