Averaging principle and optimal control for a two-time-scale stochastic reaction-diffusion HIV model
Why this work is in the frame
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Bibliographic record
Abstract
Considering the fact that free viruses replicate and spread much faster than healthy CD4 + T-cells, we propose a two-time-scale stochastic reaction-diffusion HIV model in this paper. Using the Ascoli-Arzelà theorem, we prove the tightness of the slow variable and the existence of an invariant measure that has ergodic property for the fast variable. Under certain conditions, the slow variable solution converges strongly to the solution of the averaged HIV system in the sense of \(L^{p}\) -norm ( \(p\geq 1\) ) as the time scale \(\varepsilon \to 0\) . For stochastic optimal controls of the fast-slow HIV system, the first order necessary optimality conditions are given by using the classical variational analysis approach. Simulation results show that the control strategy is effective, which can reduce the number of free viruses and increase the number of healthy CD4 + T-cells.
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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 | 0.000 | 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