Unifying incidence and prevalence under a time-varying general branching process.
J Math Biol
; 87(2): 35, 2023 08 01.
Article
em En
| MEDLINE
| ID: mdl-37526739
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.
Palavras-chave
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Doenças Transmissíveis
/
COVID-19
Tipo de estudo:
Incidence_studies
/
Prevalence_studies
/
Prognostic_studies
/
Risk_factors_studies
Limite:
Humans
Idioma:
En
Revista:
J Math Biol
Ano de publicação:
2023
Tipo de documento:
Article
País de afiliação:
Canadá