Abstract
Melanoma, the deadliest form of skin cancer, is regularly treated by surgery in conjunction with a targeted therapy or immunotherapy. Dendritic cell therapy is an immunotherapy that capitalizes on the critical role dendritic cells play in shaping the immune response. We formulate a mathematical model employing ordinary differential and delay differential equations to understand the effectiveness of dendritic cell vaccines, accounting for cell trafficking with a blood and tumor compartment. We reduce our model to a system of ordinary differential equations. Both models are validated using experimental data from melanoma-induced mice. The simplicity of our reduced model allows for mathematical analysis and admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability. We give thresholds for tumor elimination and existence. Bistability, in which the model outcomes are sensitive to the initial conditions, emphasizes a need for more aggressive treatment strategies, since the reproduction number below unity is no longer sufficient for elimination. A sensitivity analysis exhibits the parameters most significantly impacting the reproduction number, thereby suggesting the most efficacious treatments to use together with a dendritic cell vaccine.
Original language | English (US) |
---|---|
Pages (from-to) | 906-928 |
Number of pages | 23 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 80 |
Issue number | 2 |
DOIs | |
State | Published - 2020 |
Keywords
- Backward bifurcation
- Dendritic cell therapy
- Hopf bifurcation
- Partial rank correlation coefficient
- Stability analysis
ASJC Scopus subject areas
- Applied Mathematics