Dynamics and numerical analysis of a fractional-order toxoplasmosis model incorporating human and cat populations
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Toxoplasmosis is a significant zoonotic disease that poses risks to public health and animal health, making the understanding of its transmission dynamics crucial. In this study, we present a novel fractional-order model that captures complex interactions among human, cat, and mouse populations, providing deeper insights into the disease spread and control. We utilize mathematical techniques to analyze the model properties, including the existence, uniqueness, positivity, and boundedness of solutions, along with stability analysis of the equilibrium states. The basic reproduction number $R_{0}$ is derived, revealing the threshold for potential outbreaks. Our findings indicate that key parameters significantly influence the dynamics of toxoplasmosis, with implications for targeted intervention strategies. We propose the QLM-FONP numerical scheme for efficient resolution of the model and provide a comprehensive convergence analysis, demonstrating the reliability of the numerical solutions. The results confirm the effectiveness of our approach, illustrating that the proposed model not only offers accurate predictions but also extends beyond previous efforts in the literature by incorporating fractional-order dynamics, which better reflect real-world transmission processes. Overall, this study enhances the understanding of toxoplasmosis transmission and informs future research and control efforts.
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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 | 0.000 | 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