BIFURCATION ANALYSIS ON AN HIV-1 MODEL WITH CONSTANT INJECTION OF RECOMBINANT
Bibliographic record
Abstract
This paper is a continuation of our previous work on an HIV-1 therapy model of fighting a virus with another virus [Jiang et al., 2009]. The work in [Jiang et al., 2009] investigated cascading bifurcations between equilibrium solutions, as well as Hopf bifurcation from a double-infected equilibrium solution. In this paper, we propose a modification of the model in [Revilla & Garcia-Ramos, 2003; Jiang et al., 2009] by adding a constant η to the recombinant virus equation, which accounts for the treatment of constant injection of recombinants. We study the dynamics of the new model and find that η plays an important role in the therapy. Unlike the previous model without injection of recombinant, which has three equilibrium solutions, this new model can only allow two biologically meaningful equilibrium solutions. It is shown that there is [Formula: see text] depending on η, such that the HIV free equilibrium solution [Formula: see text] is globally asymptotically stable when the basic reproduction ratio, [Formula: see text]; [Formula: see text] becomes unstable when [Formula: see text]. In the latter case, there occurs the double-infection equilibrium solution, [Formula: see text], which is stable when [Formula: see text] for some [Formula: see text] larger than [Formula: see text], and loses its stability when [Formula: see text] passes the critical value [Formula: see text] and bifurcates into a family of limit cycles through Hopf bifurcation. Our results show that appropriate injection rate can help eliminate the HIV virus in the sense that the HIV free equilibrium can be made globally asymptotically stable by choosing η > 0 sufficiently large. This is in contrast to the conclusion for the case with η = 0 in which, the recombinants do not help eliminate the HIV virus but only help reduce the HIV load in the long term sense.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".