Chaotic dynamics and optimal therapeutic strategies for Caputo fractional tumor immune model in combination therapy
Bibliographic record
Abstract
In this paper, a Caputo fractional tumor immune model of combination therapy is established. First, the stability and biological significance of each equilibrium point are analyzed, and it is demonstrated that chaos may arise under specific conditions. Combined with the mathematical definition of Caputo fractional differentiation (CFD), it is found that there is a high correlation between the chaotic phenomenon of the patient's condition and the sensitivity of the patient to the change in the state of the day. The bifurcation threshold of each parameter is determined through numerical simulation, and the Hopf bifurcation of direct competition coefficient and inhibition coefficient between tumor cells and host healthy cells is elaborated upon in detail. Subsequently, a novel method combining optimal control theory with the particle swarm optimization (PSO) algorithm is proposed for the optimal control of the tumor immune model in combination therapy. Finally, the Adams-Bashforth-Moulton (ABM) prediction correction method is utilized in numerical simulations which demonstrate that the introduction of the CFD alters the model dynamics. Furthermore, these results indicate that fractional calculus can effectively be applied to tumor immune models better to elucidate complex chaotic dynamics of tumor cell evolution. Concurrently, the PSO can be successfully integrated with optimal control theory to address optimization challenges in cancer treatment.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".