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.

Department of Industrial Engineering Faculty of Engineering and Natural Sciences Kadir Has University Istanbul Turkey

See more in PubMed

CMAJ. 2010 Feb 9;182(2):131-6 PubMed

PLoS Med. 2005 Jul;2(7):e174 PubMed

Proc Natl Acad Sci U S A. 2009 Dec 22;106(51):21825-9 PubMed

J Infect Dis. 2012 Dec 15;206 Suppl 1:S94-100 PubMed

Influenza Other Respir Viruses. 2010 Jul;4(4):187-97 PubMed

BMC Med. 2009 Sep 03;7:43 PubMed

PLoS Comput Biol. 2011 Sep;7(9):e1002205 PubMed

J R Soc Interface. 2011 Jun 6;8(59):856-67 PubMed

PLoS Med. 2010 Jun 01;7(6):e1000275 PubMed

IMA J Math Appl Med Biol. 1992;9(2):67-106 PubMed

Euro Surveill. 2010 Jun 17;15(24): PubMed

Proc Natl Acad Sci U S A. 2009 Dec 22;106(51):21484-9 PubMed

PLoS Med. 2009 Dec;6(12):e1000207 PubMed

Math Biosci. 1999 Sep;160(2):191-213 PubMed

Arch Iran Med. 2009 Nov;12(6):533-41 PubMed

Influenza Other Respir Viruses. 2009 Nov;3(6):267-76 PubMed

PLoS One. 2011;6(6):e21287 PubMed

PLoS One. 2011;6(5):e19616 PubMed

Math Biosci. 1995 Feb;125(2):155-64 PubMed

J R Soc Interface. 2007 Feb 22;4(12):155-66 PubMed

Emerg Infect Dis. 2009 Dec;15(12):2004-7 PubMed

BMC Infect Dis. 2014 Jun 10;14:317 PubMed

Biometrics. 2006 Dec;62(4):1170-7 PubMed

Nature. 1979 Aug 2;280(5721):361-7 PubMed

PLoS One. 2011;6(5):e17835 PubMed

Math Biosci. 2003 Sep;185(1):15-32 PubMed