Global Stability of a Delayed HIV Model Incorporating Cytokine Effects and Impaired Immune Responses
Bibliographic record
Abstract
A mathematical model describing HIV infection influenced by inflammatory cytokines and weakened adaptive immune responses is formulated and analyzed. The system is represented by delay differential equations that characterize the interactions among uninfected CD4+T cells, infected CD4+T cells, inflammatory cytokines, HIV particles, cytotoxic T lymphocytes (CTLs), and antibodies. The model incorporates three forms of distributed delays: (i) a delay associated with the infection of healthy CD4+T cells, (ii) a delay representing the activation of cytokine responses, and (iii) a delay corresponding to the maturation period of new HIV virions. The model’s biological plausibility is verified by demonstrating essential properties of the solutions, including their non-negativity and ultimate boundedness. The basic reproduction number, R0, is computed and serves as a threshold parameter governing the existence and stability of the system’s equilibrium points. Global stability of both equilibrium states is rigorously analyzed through the construction of Lyapunov functionals. To confirm the analytical results, numerical experiments are carried out, accompanied by a sensitivity study of R0 to examine how variations in essential parameters affect the system. The impact of increased impairment of the adaptive immune response, as well as the delay time, on the progression of viral activity within the body has been discussed. Our findings indicate that, the greater the impairment in adaptive immune response, the more the virus progresses within the body, worsening the patient’s condition. Conversely, an increase in the delay time leads to suppression of viral growth.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".