Complex dynamic behaviors of a tumor-immune system with two delays in tumor actions
Why this work is in the frame
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Bibliographic record
Abstract
<p style='text-indent:20px;'>The action of a tumor on the immune system includes stimulation and neutralization, which usually have different time delays. In this work we propose a tumor-immune system to incorporate these two kinds of delays due to tumor actions. We explore effects of time delays on the model and find some different phenomena induced by them. When there is only the neutralization delay, the model has a uniform upper bound while when there is only the stimulation delay, the bound varies with the delay. The theoretic analysis suggests that, for the model only with the stimulation delay, the stability of its tumor-present equilibrium may change at most once as the delay increases, but the increase of the neutralization delay may lead to multiple stability switches for the model only with the neutralization delay. Numerical simulations indicate that, in the presence of the neutralization delay, the stimulation delay may induce multiple stability switches. Further, when the model has two tumor-present equilibria, numerical simulations also demonstrate that the model may present some interesting outcomes as each of the two delays increases. These phenomena include the onset of the cytokine storm, the almost global attractivity of the tumor-free equilibrium for sufficiently large time delays, and so on. These results show the complexity of the dynamic behaviors of the model and different effects of the two time delays.</p>
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it