Stability Properties and Hopf Bifurcation of a Delayed HIV Dynamics Model with Saturation Functional Response, Absorption Effect and Cure Rate
Bibliographic record
Abstract
In this paper, stability properties of an HIV infection model with saturation functional response, logistic proliferation term of susceptible CD4+T cells, cure rate of infected CD4+T cell, virus absorption effect, intracellular delay, and maturation delay are investigated. According to our mathematical analysis, the basic reproduction number R0 of the model completely determines its stability features. Using the characteristic equation of the model, we establish that the infection-free equilibrium point and the infected equilibrium point are locally asymptotically stable when R0 ≤ 1 and R0 > 1, respectively. By means of appropriate Lyapunov functionals and LaSalle’s invariance principle for delay models, if R0 ≤ 1, we study the global asymmetric stability of the infection-free equilibrium point of the model. When R0 > 1, we establish the occurrence of Hopf bifurcations and determine conditions for the permanence of the model. Finally, numerical simulations are also presented to confirm the analytical results.
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How this classification was reachedexpand
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 | 0.000 |
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 teacher head, 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".