Evidence map›Paper›PMID 40739114›Full record

ArticleScientific reports2025

Modeling COVID-19 transmission: effects of age structure and vaccination.

Sajjad Ali, Salah Boulaaras, Nigar Ali, Imtiaz Ahmad, Asaf Khan, Zahid Ullah

Abstract read
PubMed Full text at PMC Publisher
In one paragraph

Article in Scientific reports, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

0numbers the graph read from it
0cells of the map it votes in
1citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

1 citing paper in PubMed.

  1. Article
4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

6 authors.

Sajjad AliDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan.
Salah BoulaarasDepartment of Mathematics, College of Science, Qassim University, Buraydah, 52571, Saudi Arabia. s.boularas@qu.edu.sa.
Nigar AliDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan.
Imtiaz AhmadDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan.
Asaf KhanDepartment of Mathematics and Statistics, University of Swat, Charbagh, Khyber Pakhtunkhwa, Pakistan.
Zahid UllahDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

A mathematical model for COVID-19 dynamics is developed, incorporating age structure, disease progression, and vaccination. Addressing gaps in existing literature, the model integrates heterogeneous intercohort mixing for realistic disease transmission, with a primary focus on Pakistan and global applicability. Well-posedness is established via the abstract Cauchy problem framework. Threshold parameters and stability analysis identify conditions for disease persistence or eradication. An age-free sub-model gives additional insights. Numerical simulations using the finite differences method confirm analytical results. The study shows the crucial role of age structure and vaccination in controlling COVID-19. It provides a strong mathematical foundation for effective public health strategies.

Indexed as

COVID-19COVID-19 VaccinesModels, TheoreticalVaccinationAdultAge FactorsComputer SimulationHumansMiddle AgedPakistanSARS-CoV-2COVID-19 VaccinesAbstract Cauchy problemAge-structured modelCOVID-19 dynamicsHeterogeneous mixing intercohort mixingNumerical simulationsStability analysisVaccinationWell-posedness

Identifiers

PMID40739114
PMCPMC12311134

What OpenQuestion holds

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Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.