Impact of delay on HIV-1 dynamics of fighting a virus withanother virus
Bibliographic record
Abstract
In this paper, we propose a mathematical model for HIV-1 infectionwith intracellular delay. The model examines a viral-therapy for controllinginfections through recombining HIV-1 virus with a genetically modifiedvirus. For this model, the basic reproduction number $\mathcal{R}_0$are identified and its threshold properties are discussed.When $\mathcal{R}_0 < 1$, the infection-free equilibrium $E_0$ is globallyasymptotically stable. When $\mathcal{R}_0 > 1$, $E_0$ becomesunstable and there occurs the single-infection equilibrium $E_s$,and $E_0$ and $E_s$ exchange their stability at the transcriticalpoint $\mathcal{R}_0 =1$.If $1< \mathcal{R}_0 < R_1$, where $R_1$ is a positive constant explicitlydepending on the model parameters, $E_s$ is globally asymptotically stable,while when $\mathcal{R}_0 > R_1$, $E_s$ loses itsstability to the double-infection equilibrium $E_d$.There exist a constant $R_2$ such that $E_d$ is asymptoticallystable if $R_1<\mathcal R_0 < R_2$, and $E_s$ and $E_d$ exchange theirstability at the transcritical point $\mathcal{R}_0 =R_1$.We use one numerical exampleto determine the largest range of $\mathcal R_0$ for the localstability of $E_d$ and existence of Hopf bifurcation. Some simulationsare performed to support the theoretical results.These results show that the delay plays animportant role in determining the dynamic behaviour of the system.In the normal range of values, the delay may change the dynamic behaviourquantitatively, such as greatly reducing the amplitudes of oscillations,or even qualitatively changes the dynamical behaviour such as revokingoscillating solutions to equilibrium solutions.This suggests that the delay is a very importantfact which should not be missed in HIV-1 modelling.
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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) | 0.002 | 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".