Optimal control of an impulsive VS-EIAR epidemic model with applications to COVID-19
Bibliographic record
Abstract
In this paper, we investigate a VS-EIAR epidemiological model that incorporates vaccinated individuals {V i : i = 1, . . ., n}, where n ∈ N * .The dynamics of the VS-EIAR model are governed by a system of ordinary differential equations describing the evolution of vaccinated, susceptible, exposed, infected, asymptomatic, and deceased population groups.Our primary objective is to minimize the number of susceptible, exposed, infected, and asymptomatic individuals by administering vaccination doses to susceptible individuals and providing treatment to the infected population.To achieve this, we employ optimal control theory to regulate the epidemic dynamics within an optimal terminal time τ * .Using Pontryagin's Maximum Principle (PMP), we establish the existence of an optimal control pair (v * (t), u * (t)).Additionally, we extend the model to an impulsive VS-EIAR framework, with particular emphasis on the impact of immigration and population movement.Finally, we present numerical simulations to validate the theoretical results and demonstrate their practical applicability.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 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) | 0.002 | 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".