Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate
Bibliographic record
Abstract
An epidemic model with a generalized non-linear incidence is extended to incorporate the effect of an infection-dependent removal strategy, which is defined as a function of the number of infected individuals. It is assumed that the removal rate decreases from a maximum capacity for removing infected individuals as their number increases. The existence and stability of the associated equilibria are analysed, and the basic reproductive number (R0) is formulated. It is shown that R0 is independent of the functional form of the incidence, but depends on the removal rate. Normal forms are derived to show the different types of bifurcation the model undergoes, including transcritical, generalized Hopf (Bautin), saddle-node and Bogdanov-Takens. A degenerate Hopf bifurcation at the Bautin point, where the first Lyapunov coefficient vanishes, is discussed. Sotomayor's theorem is applied to establish a saddle-node bifurcation at the turning point of backward bifurcation. The Bogdanov-Takens normal form is derived, from which the local bifurcation curve for a family of homoclinic orbits is formulated. Bifurcation diagrams and numerical simulations, using parameter values estimated for some infectious diseases, are also presented to provide more intuition to the theoretical findings. The results show that sufficiently increasing the removal rate can reduce R0 below a subthreshold domain, which leads to disease eradication.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| 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".