| Abstract: |
| We formulate a tumor-immune interaction model with a constant delay (time needed for
a dendritic cell to become an effector cell) to capture the behavior following application of
a dendritic cell therapy. The model is validated using experimental data from melanoma-
induced mice. Through theoretical and numerical analyses, the model is shown to produce
rich dynamics, such as a Hopf bifurcation and bistability. We provide thresholds for tumor
existence and, in a special case, tumor elimination. Our work indicates a sensitivity in
model outcomes to the immune response time. We provide a stability analysis for the high
tumor equilibrium. For small delays in response, the tumor and immune system coexist at
a low level. Large delays give rise to fatally high tumor levels. Our computational and
theoretical work reveals that there exists an intermediate region of delay that generates
complex oscillatory, even chaotic, behavior. The model then reflects uncertainty in treatment
outcomes for varying initial tumor burdens, as well as tumor dormancy followed by uncontrolled
growth to a lethal size, a phenomenon seen in vivo. Theoretical and computational analyses
suggest efficacious treatments to use in conjunction with the dendritic cell vaccine. Analysis of
a highly aggressive tumor confirms the importance of representation with a time delay, as
periodic solutions are generated when a delay is present. |
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