Dynamic analysis of delayed vaccination process along with impact of retrial queues
Bibliographic record
Abstract
Abstract An unprecedented and precise time-scheduled rollout for the vaccine is needed for an effective vaccination process. This study is based on the development of a novel mathematical model considering a delay in vaccination due to the inability to book a slot in one go for a system. Two models are proposed which involve a delay differential equation mathematical model whose dynamical analysis is done to show how the delay in vaccination can destabilize the system. Further, this delay led to the formulation of a queuing model that accounts for the need to retry for the vaccination at a certain rate as delay in vaccination can have negative repercussions. The transition rates from one stage to another follow an exponential distribution. The transient state probabilities of the model are acquired by applying the Runge-Kutta method and hence performance indices are also obtained. These performance measures include the expected number of people in various states. Finally, numerical analysis is also provided to validate both models. Our results would specifically focus on what happens if the delay time increases or if the retrial rate increases (delay time decreases). The results reveal that a delay in being vaccinated by the first dose (i.e., 80 days) leads to an unstable system whereas there exists a delay simultaneously in getting vaccinated by both doses that destabilize the system early (i.e., 80 and 120 days for dose one and two, respectively). The system destabilizes faster in the presence of a delay for slot booking for both doses as compared to one dose delay. Further, the numerical results of queuing models show that if the retrial rate increases in this delay time to book the slots, it not only increases in the vaccinated class but also increases the recovered population.
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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 | 0.003 |
| 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) | 0.003 | 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".