A generalized distributed delay model of COVID-19: An endemic model with immunity waning
Bibliographic record
Abstract
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target the epidemic phase of the disease. The development of safe and effective vaccines against SARS-CoV-2 brought hope of safe reopening of schools and businesses and return to pre-COVID normalcy, until mutant strains like the Delta and Omicron variants, which are more infectious, emerged. A few months into the pandemic, reports of the possibility of both vaccine- and infection-induced immunity waning emerged, thereby indicating that COVID-19 may be with us for longer than earlier thought. As a result, to better understand the dynamics of COVID-19, it is essential to study the disease with an endemic model. In this regard, we developed and analyzed an endemic model of COVID-19 that incorporates the waning of both vaccine- and infection-induced immunities using distributed delay equations. Our modeling framework assumes that the waning of both immunities occurs gradually over time at the population level. We derived a nonlinear ODE system from the distributed delay model and showed that the model could exhibit either a forward or backward bifurcation depending on the immunity waning rates. Having a backward bifurcation implies that $ R_c < 1 $ is not sufficient to guarantee disease eradication, and that the immunity waning rates are critical factors in eradicating COVID-19. Our numerical simulations show that vaccinating a high percentage of the population with a safe and moderately effective vaccine could help in eradicating COVID-19.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".