A Second Order NSFD Method for a Malaria Propagation Model
Bibliographic record
Abstract
Standard numerical methods such as the implicit and explicit Euler and the Runge-Kutta methods have been used to approximate solutions of continuous-time transmission dynamics of many diseases. However, their convergence is conditional. Also, they do not always preserve the key features of the continuous-time model. Most times, they require a small time step which may increase the computational complexities especially for a long time horizon. In this paper we construct a nonstandard finite difference (NSFD) method to approximate the solution of a malaria propagation model. NSFD methods do not suffer from the drawback of time step restriction and preserve the physics of the problem under consideration. However their accuracy and rate of convergence remain a point of concern. In the construction of the NSFD scheme that we propose, we consider weights and denominator functions that depend not only on the time step but also iteratively on the state variables of the discrete model. This guarantees a second order convergence as opposed to earlier NSFD schemes which were independent of weights and their denominator functions were solely dependent of the time step. Numerical experiments confirm that the proposed scheme outperforms the first order NSFD in terms of accuracy and rate of convergence.
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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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".