On the uniqueness of epidemic models fitting a normalized curve of removed individuals

Journal of Mathematical Biology

Volumn 71, Issue 4, 2015, Pages 767-794

  Bilge, Ayse Humeyra ^a   Samanlioglu, Funda ^a   Ergonul, Onder ^b  

^a KADIR HAS UNIVERSITY   (Turkey)

^b KOÇ UNIVERSITY   (Turkey)

Author keywords

Dynamical systems; Epidemic models; Fatality data; Inference; SEIR model; SIR model

Indexed keywords

BIOLOGICAL MODEL; COMPUTER SIMULATION; CZECH REPUBLIC; EPIDEMIC; HUMAN; INFLUENZA A VIRUS (H1N1); INFLUENZA, HUMAN; MATHEMATICAL PHENOMENA; PANDEMIC; SEASON; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; TURKEY;

COMPUTER SIMULATION; CZECH REPUBLIC; EPIDEMICS; HUMANS; INFLUENZA A VIRUS, H1N1 SUBTYPE; INFLUENZA, HUMAN; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; PANDEMICS; SEASONS; TURKEY;

EID: 84941336130     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-014-0838-z     Document Type: Article

References (38)

1. Anderson RM, May RM (1979) Population biology of infectious diseases: part I. Nature 280:361–367
2. Balcan D, Colizza V, Goncalves B, Hu H, Ramasco JJ, Vespignani A (2009) Multiscale mobility networks and the spatial spreading of infectious diseases. Proc Natl Acad Sci USA 106(51):21484–21489
3. Barakat A, Ihazmad H, El Falaki F, Tempia S, Cherkaoui I, El Aouad R (2012) 2009 Pandemic influenza A virus subtype H1N1 in Morocco, 2009–2010: epidemiology, transmissibility, and factors associated with fatal cases. J Infect Dis 206(1):S94–S100
4. Bilge AH, Samanlioglu F, Ergonul O (2012) A susceptible-exposed-infected-removed (SEIR) model for the 2009–2010 A/H1N1 epidemic in Istanbul. arXiv:1205.2497v1 [q-bio.QM]
5. Boni MF, Manh BH, Thai PQ, Farrar J, Hien TT, Kinh NV, Horby P (2009) Modelling the progression of pandemic influenza A (H1N1) in Vietnam and the opportunities for reassortment with other influenza viruses. BMC Med 7:43
6. Chowell G, Nishiura H, Bettencourt LMA (2007) Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J R Soc Interf 4:155–166
7. Chowell G, Viboud C, Munayco CV, Gomez J, Simonsen L, Miller MA, Tamerius J, Fiestas V, Halsey ES, Laguna-Torres VA (2011) Spatial and temporal characteristics of the 2009 A/H1N1 influenza pandemic in Peru. Plos One 6(6):Article number e21287
8. Coelho FC, Codeco CT, Gomes MGM (2011) A Bayesian framework for parameter estimation in dynamical models. Plos One 6(5):e19616
9. Crow EL, Shimizu K (1988) Lognormal distributions:theory and applications. Marcel Dekker, New York
10. Diekmann O, Heesterbeek H, Britton T (2012) Mathamatical tools for understanding infectious disease dynamics. Princeton series in theoretical and computational biology
11. Ergönül Ö, Alan S, Ak Ö, Sargın F, Kantürk A, Gündüz A, Engin D, Öncül O, Balkan II, Ceylan B, Benzonana N, Yazıcı S, Şimşek F, Uzun N, Inan A, Gulhan E, Ciblak M, Midilli K, Ozyurt M, Badur S, Gencer S, Nazlıcan O, Özer S, Özgüneş N, Yıldırmak T, Aslan T, Göktaş P, Saltoǧlu N, Fincancı M, Dokucu AI, Eraksoy H, Turkish Society of Clinical Microbiology and Infectious Diseases (KLIMIK) Pandemic Influenza Study Group (2014) Predictors of fatality in pandemic influenza A (H1N1) virus infection among adults. BMC Infect Dis. 14(1):317. doi:10.1186/1471-2334-14-317
12. Goldstein E, Dushoff J, Ma J, Plotkin JB, Earn DJ, Lipsitch M (2009) Reconstructing influenza incidence by deconvolution of daily mortality time series. PNAS 106:21825–21829
13. Greenhalgh D (1992) Some results for a SEIR epidemic model with density dependence in the death rate. IMA J Math Appl Med Biol 9:67
14. Haghdoost AA, Gooya MM, Baneshi MR (2009) Modelling of H1N1 flu in Iran. Arch Iran Med 12(6):533–541
15. Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev. 42:599–653
16. Hsieh YH (2010) Pandemic influenza A (H1N1) during winter influenza season in the southern hemisphere. Influ Respir Virus 4(4):187–197
17. Jesan T, Menon GI, Sinha S (2011) Epidemiological dynamics of the 2009 influenza A(H1N1) outbreak in India. Curr Sci 100(7):1051–1054
18. Katriel G, Yaari R, Huppert A, Roll U, Stone L (2011) Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study. J R Soc Interf 8(59):856–867
19. Kermack WO, McKendrick AG (1927) Contributions to the theory of epidemics-I. Proc R Soc 115A:700–721. (Reprinted in Bulletin of Mathematical Biology 1991; 53(1–2):33–55)
20. Lekone PE, Finkenstadt BF (2006) Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62:1170–1177
21. Li MY, Muldowney JS (1995) Global stability for the SEIR model in epidemiology. Math Biosci 125(2):155–164
22. Li MY, Muldowney JS, Van Den Driessche P (1999a) Global stability of SEIRS models in epidemiology. Can Appl Math Q 7(4):409–425
23. Li MY, Graef JR, Wang L, Karsai J (1999b) Global dynamics of a SEIR model with varying total population size. Math Biosci 160:191–213
24. Li MY, Smith HL, Wang L (2001) Global dynamics of an SEIR epidemic model with vertical transmission. SIAM J Appl Math 62:58
25. Li G, Jin Z (2005) Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period. Chaos Solitons Fractals 25:1177–1184
26. Merler S, Ajelli M, Pugliese A, Ferguson NM (2011) Determinants of the spatiotemporal dynamics of the 2009 H1N1 pandemic in Europe: implications for real-time modelling. Plos Comput Biol 7(9):e1002205
27. Navarro-Robles E, Martinez-Matsushita L, Lopez-Molina R, Fritz-Hernandez J, Flores-Aldana BA, Mendoza-Perez JC (2012) Model to estimate epidemic patterns of influenza A (H1N1) in Mexico. Revista PanAmericana de Salud Publica-Pan. Am J Public Health 31(4):269–274
28. Paine S, Mercer GN, Kelly PM, Bandaranayake D, Baker MG, Huang QS, Mackereth G, Bissielo A, Glass K, Hope V (2010) Transmissibility of 2009 pandemic influenza A(H1N1) in New Zealand: effective reproduction number and influence of age, ethnicity and importations. Eurosurveillance 15(24):9–17
29. Presanis AM, De Angelis D, The New York City Swine Flu Investigation Team, Hagy A, Reed C, Riley S, Cooper BS, Finelli L, Biedrzycki P, Lipsitch M (2009) The severity of pandemic H1N1 influenza in the United States, from April to July 2009: a Bayesian analysis. PLoS Medicine 6(12):1–12. www.plosmedicine.org
30. Reed C, Angulo FJ, Swerdlow DL, Lipsitch M, Meltzer MI, Jernigan D, Finelli L (2009) Estimates of the prevalence of pandemic (H1N1) 2009, United States, April–July 2009. Emerg Infect Dis 15(12):2004–2007
31. Roberts MG, Nishiura H (2011) Early estimation of the reproduction number in the presence of imported cases: pandemic influenza H1N1-2009 in New Zealand. Plos One 6(5):Article number e17835
32. Shu H, Fan D, Wei J (2012) Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission. Nonlinear Anal Real World Appl 13(4):1581–1592
33. Trottier H, Philippe P (2002) Deterministic modeling of infectious diseases: applications to measles and other similar infections. Intern J Infect Dis 2(1)
34. Tuite AR, Greer AL, Whelan M, Winter AL, Lee B, Yan P, Wu JH, Moghadas S, Buckeridge D, Pourbohloul B, Fisman DN (2010) Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza. Can Med Assoc J 182(2):128–133
35. Van Kerkhove MD, Asikainen T, Becker NG, Bjorge S, Desenclos J, dos Santos T, Fraser C, Leung GM, Lipsitch M, Longini Jr IM, McBryde ES, Roth CE, Shay DK, Smith DJ, Wallinga J, White PJ, Ferguson NM, Riley S for the WHO Informal Network for Mathematical Modelling for Pandemic Influenza H1N1 2009 (Working Group on Data Needs) (2010) Studies needed to address public health challenges of the 2009 H1N1 influenza pandemic: insights from modeling. PLoS Medicine 7(6):1–6. www.plosmedicine.org
36. Wearing HJ, Rohani P, Keeling MJ (2005) Appropriate models for the management of infectious diseases. PLoS Medicine 2(7):e621–e627. www.plosmedicine.org
37. White LF, Wallinga J, Finelli L, Reed C, Riley S, Lipsitch M, Pagano M (2009) Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA. Influ Respir Virus 3(6):267–276
38. Zhang J, Ma Z (2003) Global dynamics of an SEIR epidemic model with saturating contact rate. Math Biosci 185:15–32