Abstract:

We formulate a mathematical model simulating the effect of a patient's immune response in controlling chronic myelogenous leukemia (CML). The data, collected at Stanford Medical School, shows that an anti-leukemia T cell response initiates shortly after the patient enters remission under Gleevec treatment. By analyzing the model, we hypothesize that cancer vaccinations may sustain the anti-leukemia T cell response and potentially eliminate all residual leukemia cells for a durable cure.

In formulating the model, we begin with the system of ordinary differential equations from Michor et al. to account for the dynamics of Gleevec treatment and incorporate the delay differential equation paradigm of DeConde et al. to account for the dynamics of the T cell response. Using this combined model, we simulate the effects of cancer vaccinations on the leukemia population.

We conduct a stability analysis with respect to the delay parameter and determine the range of delay values that correspond to asymptotically stable solutions. Based on the model simulations and stability analysis, we discuss the potential for strategic treatment interruptions (STIs) to enhance the effectiveness of the combined Gleevec and cancer vaccination strategy.

References

DeConde, R., Kim, P.S., Levy, D., Lee, P.P. Post-transplantation dynamics of the immune response to chronic myelogenous leukemia. J Theor Biol. 2005. 236(1): pp. 39-59.

Michor, F., Hughes, T.P., Iwasa, Y., Branford, S., Shah, N.P., Sawyers, C.L., Nowak, M.A. Dynamics of chronic myeloid leukaemia. Nature. 2005 435(7046):pp. 1267