Mathematical modelling of cancer stem cell-targeted immunotherapy

•Mathematical modelling of the interactions of cancer stem cells (CSCs), non-CSCs, cytotoxic T-cells (CTCs), and dendritic cells (DCs) to replicate the following experimental results: Grafting mice with CSCs produces more, and larger tumors than transfusing mice with nCSCs. Giving mice dendritic cell vaccines or CTC treatment prepared with CSCs is more effective than giving mice CTC treatment prepared with nCSCs.•Mathematical modelling of how chemotherapy and immunotherapy could work together to minimize tumor size and future tumor growth: Although chemotherapy is more effective at reducing current tumor burden, CSC-specific therapy reduces tumorogenicity, and decreases future tumor burden. The cancer stem cell hypothesis states that tumors are heterogeneous and comprised of several different cell types that have a range of reproductive potentials. Cancer stem cells (CSCs), represent one class of cells that has both reproductive potential and the ability to differentiate. These cells are thought to drive the progression of aggressive and recurring cancers since they give rise to all other constituent cells within a tumor. With the development of immunotherapy in the last decade, the specific targeting of CSCs has become feasible and presents a novel therapeutic approach. In this paper, we construct a mathematical model to study how specific components of the immune system, namely dendritic cells and cytotoxic T-cells interact with different cancer cell types (CSCs and non-CSCs). Using a system of ordinary differential equations, we model the effects of immunotherapy, specifically dendritic cell vaccines and T-cell adoptive therapy, on tumor growth, with and without chemotherapy. The model reproduces several results observed in the literature, including temporal measurements of tumor size from in vivo experiments, and it is used to predict the optimal treatment schedule when combining different treatment modalities. Importantly, the model also demonstrates that chemotherapy increases tumorigenicity whereas CSC-targeted immunotherapy decreases it.