ArticleJournal of mathematical biology2015
On the uniqueness of epidemic models fitting a normalized curve of removed individuals.
Article in Journal of mathematical biology, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Underdetection in a stochastic SIR model for the analysis of the COVID-19 Italian epidemic.Stochastic environmental research and risk assessment : research journal · 2022Article
- What Can We Estimate From Fatality and Infectious Case Data Using the Susceptible-Infected-Removed (SIR) Model? A Case Study of Covid-19 Pandemic.Frontiers in medicine · 2020Article
- An Overview of the 2009 A(H1N1) Pandemic in Europe: Efficiency of the Vaccination and Healthcare Strategies.Journal of healthcare engineering · 2016Review
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3 authors.
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Abstract
The susceptible-infected-removed (SIR) and the susceptible-exposed-infected-removed (SEIR) epidemic models with constant parameters are adequate for describing the time evolution of seasonal diseases for which available data usually consist of fatality reports. The problems associated with the determination of system parameters starts with the inference of the number of removed individuals from fatality data, because the infection to death period may depend on health care factors. Then, one encounters numerical sensitivity problems for the determination of the system parameters from a correct but noisy representative of the number of removed individuals. Finally as the available data is necessarily a normalized one, the models fitting this data may not be unique. We prove that the parameters of the (SEIR) model cannot be determined from the knowledge of a normalized curve of "Removed" individuals and we show that the proportion of removed individuals, [Formula: see text], is invariant under the interchange of the incubation and infection periods and corresponding scalings of the contact rate. On the other hand we prove that the SIR model fitting a normalized curve of removed individuals is unique and we give an implicit relation for the system parameters in terms of the values of [Formula: see text] and [Formula: see text], where [Formula: see text] is the steady state value of [Formula: see text] and [Formula: see text] and [Formula: see text] are the values of [Formula: see text] and its derivative at the inflection point [Formula: see text] of [Formula: see text]. We use these implicit relations to provide a robust method for the estimation of the system parameters and we apply this procedure to the fatality data for the H1N1 epidemic in the Czech Republic during 2009. We finally discuss the inference of the number of removed individuals from observational data, using a clinical survey conducted at major hospitals in Istanbul, Turkey, during 2009 H1N1 epidemic.
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