Backward bifurcation, basic reinfection number and robustness of an SEIRE epidemic model with reinfection
Why this work is in the frame
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Bibliographic record
Abstract
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds [Formula: see text] (the basic reproduction number) and [Formula: see text] (a threshold less than one). Our investigations show that when [Formula: see text], the system has an endemic equilibrium, which is globally asymptotically stable. When [Formula: see text], the epidemic system exhibits bistable dynamics. That is, the system has backward bifurcation and the disease cannot be eradicated. In order to eradicate the disease, we must ensure that the basic reproduction number [Formula: see text] is less than [Formula: see text]. The basic reinfection number is obtained to measure the reinfection force, which turns out to be a new tipping point for disease dynamics. We also give definition of robustness, a new concept to measure the difficulty of completely eliminating the disease for a bistable epidemic system. Numerical simulations are carried out to verify the conclusions.
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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 | 0.000 |
| 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 it