Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
Bibliographic record
Abstract
Infectious diseases have been one of the major causes of human mortality, and mathematical models have been playing significant roles in understanding the spread mechanism and controlling contagious diseases. In this paper, we propose a delayed SEIR epidemic model with intervention strategies and recovery under the low availability of resources. Non-delayed and delayed models both possess two equilibria: the disease-free equilibrium and the endemic equilibrium. When the basic reproduction number $ R_0 = 1 $, the non-delayed system undergoes a transcritical bifurcation. For the delayed system, we incorporate two important time delays: $ \tau_1 $ represents the latent period of the intervention strategies, and $ \tau_2 $ represents the period for curing the infected individuals. Time delays change the system dynamics via Hopf-bifurcation and oscillations. The direction and stability of delay induced Hopf-bifurcation are established using normal form theory and center manifold theorem. Furthermore, we rigorously prove that local Hopf bifurcation implies global Hopf bifurcation. Stability switching curves and crossing directions are analyzed on the two delay parameter plane, which allows both delays varying simultaneously. Numerical results demonstrate that by increasing the intervention strength, the infection level decays; by increasing the limitation of treatment, the infection level increases. Our quantitative observations can be useful for exploring the relative importance of intervention and medical resources. As a timing application, we parameterize the model for COVID-19 in Spain and Italy. With strict intervention policies, the infection numbers would have been greatly reduced in the early phase of COVID-19 in Spain and Italy. We also show that reducing the time delays in intervention and recovery would have decreased the total number of cases in the early phase of COVID-19 in Spain and Italy. Our work highlights the necessity to consider the time delays in intervention and recovery in an epidemic model.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| 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".