Mathematical modelling of the dynamics of prostate cancer with a curative vaccine

Abstract

A mathematical model for prostate cancer treatment using a curative vaccine is developed to determine the efficacy of constant drug infusion into the body tissues. It describes the interaction of prostate tumour cells, immune response, and treatment using the curative vaccine, commonly known as the Sipuleucel-T vaccine. Stability analysis of the model shows that, without treatment, prostate tumour cells would grow to the maximum carrying capacity. It is also demonstrated that the vaccine could clear prostate tumour cells from the body tissues if the curative vaccine efficacy is less than the ratio of the product of death of dendritic cells and its decay rate to the activation rate of the therapy. Global sensitivity analysis is investigated to establish critical factors that promote prostate cancer recurrence during treatment. Further analysis suggests that the recruitment rate of effector cells by dendritic cells, which leads to an increase in lysis of prostate tumour cells determines the curative vaccine’s success. Numerical simulations show that when the curative vaccine is administered at minimum doses, androgen-independent cancer cells take a long time to be eliminated from the body tissue. At the same time, they can be cleared in a short period when a standard or higher dose is administered. The use of a standard dose is preferable as it lowers the side effects, although the treatment period would be relatively long.

Keywords

• Qualitative analysis
• Sensitivity analysis
• Androgen dependent and independent cancer cells
• Sipuleucel
• Dendritic cells and Eeffector cells