title: A theoretical framework to identify invariant thresholds in infectious disease epidemiology.
abstract: Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena - such as the epidemic and reinfection thresholds - remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems.
authors: CIBIO-InBIO, Centro de Investigação em Biodiversidade e Recursos Genéticos, Universidade do Porto, Portugal; Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil; Liverpool School of Tropical Medicine, United Kingdom. Electronic address: Gabriela.Gomes@lstmed.ac.uk.
authors: M Gabriela M
authors: MGM
authors: Gomes
authors: Instituto Gulbenkian de Ciência, Oeiras, Portugal.
authors: Erida
authors: E
authors: Gjini
authors: Instituto Gulbenkian de Ciência, Oeiras, Portugal.
authors: Joao S
authors: JS
authors: Lopes
authors: Instituto Gulbenkian de Ciência, Oeiras, Portugal.
authors: Caetano
authors: C
authors: Souto-Maior
authors: Departamento de Matemática e Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Universidade de Lisboa, Portugal.
authors: Carlota
authors: C
authors: Rebelo
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D006801:Humans; D008954:Models, Biological
keywords: Endemic infection; Epidemic threshold; Global health; Heterogeneity; Reinfection threshold