  We introduce a set of ordinary differential equations (ODE) that
qualitatively reproduces delayed responses observed in immune checkpoint
blockade therapy (e.g. anti-CTLA-4 Ipilimumab). This type of immunotherapy has
been at the forefront of novel and promising cancer treatments over the past
decade and was recognised by the 2018 Nobel Prize in Medicine. Our model
describes the competition between effector T cells and non-effector T cells in
a tumour. By calibrating a small subset of parameters that control immune
checkpoint expression along with the patient's immune-system cancer readiness,
our model is able to simulate either a complete absence of patient response to
treatment, a quick anti-tumour T cell response (within days) or a delayed
response (within months). Notably, the parameter space that generates a delayed
response is thin and must be carefully calibrated, reflecting the observation
that a small subset of patients experience such reactions to checkpoint
blockade therapies. Finally, simulations predict that the anti-tumour T cell
storm that breaks the delay is very short-lived compared to the length of time
the cancer is able to stay suppressed. This suggests the tumour may subsist off
an environment hostile to effector T cells; however, these cells are -- at rare
times -- able to break through the tumour immunosuppressive defences to
neutralise the tumour for a prolonged period. Our simulations aim to
qualitatively describe the delayed response phenomenon without making precise
fits to particular datasets, which are limited. It is our hope that our
foundational model will stimulate further interest within the immunology
modelling field.
