Mathematical model establishment and simulation analysis of the spread of COVID-19 epidemic
Bibliographic record
Abstract
In order to explore the intrinsic laws of the spread of COVID-19 across the globe, this paper applies partial differential equation and related theories to model and carry out theoretical analysis and numerical analysis. Firstly, by adding the free diffusion term to the traditional ordinary differential SEIRS epidemic model, the corresponding partial differential epidemic model is established. Secondly, the basic reproduction number R0is calculated by using operator theory and spectral method, and it is testified that R0is monotonically decreasing with respect to the diffusion coefficients of the exposed and infected individuals. Furthermore, we examine the asymptotic property of the endemic equilibrium with respect to the diffusion coefficient. Finally, we take the Canadian epidemic data as an example to carry out numerical simulation and parameter sensitivity analysis by applying difference method and BP neural network, the results show that strengthening the isolation of susceptible and exposed individuals, reducing the infection rate of infected individuals will help to better control the large-scale outbreak of the epidemic.
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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 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".