Global Stability for a Diffusive Infection Model with Nonlinear Incidence
Bibliographic record
Abstract
The first purpose of this article was to establish and analyze system 4 with an abstract function incidence rate under homogeneous Neumann boundary conditions. The system models the dynamics of interactions between pathogens and the host immune system, which has important applications in HIV-1, HCV, flu etc. By the Lyapunov–LaSalle method, we obtained the globally asymptotic stability of the equilibria. Specifically speaking, by introducing the reproductive numbers R0 and R1, we showed that if R0≤1, then the infection-free equilibrium E0 is globally asymptotically stable, i.e., the virus is unable to sustain the infection and will become extinct; if R1≤1<R0, then the CTL-inactivated infection equilibrium E1 is globally asymptotically stable, i.e., the infection becomes chronic but without persistent CTL response; if R1>1, the CTL-activated equilibrium E2 is globally asymptotically stable, and the infection is chronic with persistent CTL response. Additionally, we also investigate the discretization of the model by using a non-standard finite difference scheme, and our results confirm that the global stability of the equilibria of the continuous model and the discrete model is consistent. Finally, numerical simulations are performed to illustrate the theoretical results. Our model and results are to a certain extent generalizations of and improvements upon the previous results given by Zhu, Wang.
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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 | 0.001 |
| 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".