Hopf bifurcation in a CTL-inclusive HIV-1 infection model with two time delays
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Bibliographic record
Abstract
In this paper, we investigate a delayed HIV-1 infection model with immune response. Though a logistic growth is incorporated in the growth of the target cells, our focus is on the effect of delays on the infection dynamics. We first study the existence of steady states, which depends on the basic reproduction number $R_0$. When $R_0\le 1$, there is only the infection-free steady state, which is globally asymptotically stable if $R_0 < 1$. When $R_0> 1$, besides the unstable infection-free steady state, there is a unique infected steady state. We then study the local stability of the infected steady state and local Hopf bifurcation at it. The theoretical analysis indicates that the dynamics scenario is complicated. For example, there can be three sequences of critical values, stability switches and double Hopf bifurcation can occur. Some of the theoretical results are also illustrated with numerical simulations.
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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) | 0.000 | 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 | 0.001 |
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