Impact of vaccination and nonlinear incidence rate on the dynamic of influenza strains epidemic model: Optimal control approach
Bibliographic record
Abstract
In this study, we develop and analyze a mathematical model describing the transmission dynamics of influenza strains, including both drug-resistant and non-resistant variants. Our model generalizes several existing epidemic models by incorporating key biological factors. We first prove the existence, uniqueness, positivity, and boundedness of global solutions to ensure the model is well-posed under natural conditions. Using the next-generation matrix method, we calculate two basic reproduction numbers associated with the model. We identify four biologically relevant equilibrium points: the disease-free equilibrium, the resistant endemic equilibrium, the non-resistant endemic equilibrium, and the coexistence endemic equilibrium. The local stability of these equilibrium is established through standard stability analysis techniques. Furthermore, we propose two optimal control strategies, treatment and media awareness campaigns based on Pontryagin’s Maximum Principle to reduce the spread of infection. Numerical simulations performed in Matlab illustrate and support our theoretical results. Finally, the paper concludes with a discussion and suggestions for future research directions.
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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 | 0.004 |
| 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 | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".