A mathematical framework of HIV and TB co-infection dynamics
Bibliographic record
Abstract
The biological processes involved in diseases like human immunodeficiency virus (HIV) and tuberculosis (TB) require extensive research, particularly when both diseases occur together. This piece of research delves to explore a new fractional-order mathematical model that examines the co-dynamics of HIV and TB, taking into account the treatment effects. Although no definitive vaccine or cure for HIV exists, antiretroviral therapy (ART) can slow disease spread and prevent subsequent complications. The basic properties of the fractional model in the Caputo sense, including existence, uniqueness, positivity, and boundedness, are proved using crucial mathematical tools. The disease-free and endemic equilibria are determined for the co-infection model, along with the basic reproduction numbers [Formula: see text] for TB and [Formula: see text] for HIV, using the next-generation matrix technique. A comprehensive analysis is conducted to determine the local and global stability of the disease-free equilibrium point by applying the Routh-Hurwitz criteria and constructing a Lyapunov function, respectively. The stability of the disease-free state is also verified graphically by considering different initial conditions and observing the convergence of the curves to the disease-free equilibrium point. Furthermore, the model is examined under different scenarios by varying the reproduction numbers, specifically when [Formula: see text] and [Formula: see text], and when [Formula: see text] and [Formula: see text]. Using actual data from the USA from 1999 to 2022, crucial parameters are estimated. The final fitting of the model with real data demonstrates how effectively the model framework aligns with the data. Finally, computational simulations are performed for different cases to illustrate the behavior of the model solutions by varying the fractional order derivative, as well as examining the solution's behavior with respect to the stability points.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".