Dynamic Behaviors of a Periodic System with Threshold Policy-Guided Periodic and Intermittent Therapy of Tumor
Bibliographic record
Abstract
Abstract. Recent clinical studies provide strong evidence that adaptive tumor therapy is a promising threshold policy-guided periodic and intermittent treatment for prolonging treatment efficacy particularly for prostate cancer, despite the observed tumor size fluctuations in the patients. Understanding plausible patterns of tumor size fluctuations under different treatment scenarios is important to evaluate the therapy outcomes. Here we use state-of-the-art modeling and analytic frameworks of periodic switching systems and state-dependent switching systems to develop a dynamic model that mimics the adaptive therapy, and we describe dynamical behaviors of the model system with a particular focus on the patterns of periodic fluctuation. Under the threshold policy, patients may not be given therapies during the a priori treatment period. We show that this threshold-guided treatment will give rise to a new type of periodic solutions with complex structures, characterized as [Formula: see text]-periodic solutions. We examine, both theoretically and numerically, the existence, as well as the local and global stability of such periodic solutions, including the boundary periodic solutions with one vanished compartment and positive [Formula: see text]-periodic solutions. It is hoped this study also shows the great potential in developing a class of models to describe threshold-triggered periodic and intermittent control in many fields, which in turn may generate many new dynamic behaviors of nonsmooth dynamic systems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".