Models of tumour-immune dynamics for therapies targeting small cancers
Recent advances have opened the possibility of treating some cancers by developing preventative vaccines. Such cancer vaccines would function by training a person’s immune response to recognise and eliminate early-stage tumours close to inception, by producing a memory population of immune cells against certain tumour-associated substances, called antigens. A challenge to designing preventative cancer vaccines is understanding the tumourimmune dynamics that leads to successful tumour elimination by the immune response. In this talk, Dr Frascoli will discuss some original approaches to model this dynamics. One example will be an analytically solvable ODE (toy-) model of tumour-immune dynamics for small, solid tumours. From the mathematical point of view, this approach shows the importance of tumour geometry in shaping immune eectiveness and the likelihood of eliminating the tumour. Some findings also reveal that the tumour volume must surpass a threshold size for cancer to be completely eliminated and that a tumour can become dormant if deeply infiltrated by immune cells. A second example will be a hybrid system consisting of a partial dierential equation, a delay-dierential equation and an agent-based model. The system describes the vicinity of a developing tumour and the draining lymph node, where immune cells originate. This model accounts for tumour adhesion and motility properties of cancer cells, using a probabilistic framework. Results show that adhesion and motility influence therapeutic outcomes in a complicated and often unpredictable way. Finally, some snapshots of other modelling approaches for related immune-tumour scenarios and therapies will conclude the talk.