Evidence map›Paper›PMID 37526739›Full record

ArticleJournal of mathematical biology2023

Unifying incidence and prevalence under a time-varying general branching process.

Mikko S Pakkanen, Xenia Miscouridou, Matthew J Penn, Charles Whittaker, Tresnia Berah, Swapnil Mishra, Thomas A Mellan, Samir Bhatt

Abstract read
PubMed Full text at PMC Publisher
In one paragraph

Article in Journal of mathematical biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.

0numbers the graph read from it
0cells of the map it votes in
5citing 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

5 citing papers in PubMed.

  1. Article
  2. Review
  3. Incorporating testing volume into estimation of effective reproduction number dynamics.Journal of the Royal Statistical Society. Series A, (Statistics in Society) · 2024
    Article
  4. Asymptotic Analysis of Optimal Vaccination Policies.Bulletin of mathematical biology · 2023
    Article
  5. 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

8 authors.

Mikko S Pakkanen *Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada. m.pakkanen@imperial.ac.uk.ORCID 0000-0002-0696-4914
Xenia Miscouridou *Department of Mathematics, Imperial College London, London, UK.
Matthew J Penn *Department of Statistics, University of Oxford, Oxford, UK.
Charles WhittakerDepartment of Infectious Disease Epidemiology, Imperial College London, London, UK.
Tresnia BerahDepartment of Mathematics, Imperial College London, London, UK.
Swapnil MishraDepartment of Infectious Disease Epidemiology, Imperial College London, London, UK.
Thomas A Mellan *Department of Infectious Disease Epidemiology, Imperial College London, London, UK.
Samir Bhatt *Department of Infectious Disease Epidemiology, Imperial College London, London, UK. s.bhatt@imperial.ac.uk.ORCID 0000-0002-0891-4611

Funding

Department of HealthMedical Research Council MR/R015600/1Medical Research Council MR/V038109/1Medical Research Council MR/X020258/1
6 · The paper itself

Abstract

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman-Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox.

Indexed as

Communicable DiseasesCOVID-19HumansIncidencePrevalenceSARS-CoV-2Back-calculationBranching processCOVID-19Crump–Mode–Jagers processIncidenceInhomogenous Poisson processPrevalenceRenewal equationReproduction numberTime varying reproduction number

Identifiers

PMID37526739
PMCPMC10393927

What OpenQuestion holds

Textmetadata
LicenceCC BY
Read underepoch 390

Registered trials

None linked

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.