Modelling and Optimal Control of Influenza Dynamics with Structured Populations Based on Education and Isolation
Bibliographic record
Abstract
This paper presents a new mathematical model for the transmission of avian influenza virus dynamics with education-structured susceptible and isolation-structured infectious human populations in the presence of vaccination. Several dynamical systems methodologies are employed to analyse the avian influenza in human-bird interacting populations. The fundamental properties exhibited by the model are assessed through the theory of positivity and boundedness of solutions. The effective reproduction number, Re, that measures the spread potential of the influenza infection is calculated using the next generation matrix approach. Metzler matrix approach and Lyapunov function are employed to investigate the global asymptotic dynamics of the model about its influenza-free and endemic states, respectively. Furthermore, the model is extended to accommodate four time-dependent control interventions, such as public awareness campaign, vaccination, treatment with anti-viral drugs, and birds culling strategy. By applying Pontryagin’s maximum principle, the optimal control quadruple are characterized. Specifically, combinations of any three of the control interventions are explored in forestalling the transmission of avian influenza in the population. The findings of the study do not only reveal various parameters of the model to be targeted for prevention and control of the disease, but also show the importance of consolidating control efforts in the fight against the avian influenza disease.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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".