Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis
Bibliographic record
Abstract
The resurgence of multi-drug-resistant tuberculosis in some parts of Europe and North America calls for a mathematical study to assess the impact of the emergence and spread of such strain on the global effort to effectively control the burden of tuberculosis. This paper presents a deterministic compartmental model for the transmission dynamics of two strains of tuberculosis, a drug-sensitive (wild) one and a multi-drug-resistant strain. The model allows for the assessment of the treatment of people infected with the wild strain. The qualitative analysis of the model reveals the following. The model has a disease-free equilibrium, which is locally asymptotically stable if a certain threshold, known as the effective reproduction number, is less than unity. Further, the model undergoes a backward bifurcation, where the disease-free equilibrium coexists with a stable endemic equilibrium. One of the main novelties of this study is the numerical illustration of tri-stable equilibria, where the disease-free equilibrium coexists with two stable endemic equilibrium when the aforementioned threshold is less than unity, and a bi-stable setup, involving two stable endemic equilibria, when the effective reproduction number is greater than one. This, to our knowledge, is the first time such dynamical features have been observed in TB dynamics. Finally, it is shown that the backward bifurcation phenomenon in this model arises due to the exogenous re-infection property of tuberculosis.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".