Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model

Bulletin of Mathematical Biology

Volumn 81, Issue 11, 2019, Pages 4343-4365

  Smirnova, Alexandra ^a   deCamp, Linda ^a   Chowell, Gerardo ^a  

^a GEORGIA STATE UNIVERSITY   (United States)

Author keywords

Parameter estimation; Regularization; Volterra equation

Indexed keywords

ALGORITHM; BIOLOGICAL MODEL; COMPUTER SIMULATION; DISEASE PREDISPOSITION; DISEASE TRANSMISSION; EBOLA HEMORRHAGIC FEVER; EPIDEMIC; FORECASTING; HUMAN; INCIDENCE; INFLUENZA; MARKOV CHAIN; MATHEMATICAL PHENOMENA; NONPARAMETRIC TEST; PROCEDURES; SPANISH INFLUENZA; STATISTICAL MODEL; TIME FACTOR;

ALGORITHMS; COMPUTER SIMULATION; DISEASE SUSCEPTIBILITY; DISEASE TRANSMISSION, INFECTIOUS; EPIDEMICS; FORECASTING; HEMORRHAGIC FEVER, EBOLA; HUMANS; INCIDENCE; INFLUENZA PANDEMIC, 1918-1919; INFLUENZA, HUMAN; LINEAR MODELS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; STATISTICS, NONPARAMETRIC; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 85018393850     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-017-0284-3     Document Type: Article

References (36)

1. Bakushinsky AB, Smirnova AB, Liu H (2015) A nonstandard approximation of pseudoinverse and a new stopping criterion for iterative regularization. Inverse Ill Posed Probl 23(3):195–210
2. Biggerstaff M, Alper D, Dredze M, Fox S, Fung IC, Hickmann KS, Lewis B, Rosenfeld R, Shaman J, Tsou MH et al (2016) Results from the centers for disease control and prevention’s predict the 2013–2014 Influenza Season Challenge. BMC Infect Dis 16:357
3. Bjørnstad ON, Finkenstädt BF, Grenfell BT (2002) Dynamics of measles epidemics: estimating scaling of transmission rates using a time series sir model. Ecol Monogr 72(2):169–184
4. Camacho A, Kucharski A, Aki-Sawyerr Y, White MA, Flasche S, Baguelin M, Pollington T, Carney JR, Glover R, Smout E, Tiffany A, Edmunds WJ, Funk S (2015) Temporal changes in Ebola Transmission in Sierra Leone and implications for control requirements: a real-time modelling Study. PLoS Curr. doi:10.1371/currents.outbreaks.406ae55e83ec0b5193e30856b9235ed2
5. Capistrán MA, Moreles MA, Lara B (2009) Parameter estimation of some epidemic models. The case of recurrent epidemics caused by respiratory syncytial virus. Bull Math Biol 71(8):1890–1901
6. Cauchemez S, Valleron A-J, Boelle P-Y, Flahault A, Ferguson NM (2008) Estimating the impact of schoolclosure on influenza transmission from sentinel data. Nature 452(7188):750–754
7. Chowell G, Hengartner NW, Castillo-Chavez C, Fenimore PW, Hyman JM (2004) The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. J Theor Biol 229(1):119–126
8. Chowell G, Nishiura H, Bettencourt LM (2007) Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J R Soc Interface R Soc 4(12):155–166
9. Chowell G, Sattenspiel L, Bansal S, Viboud C (2016) Mathematical models to characterize early epidemic growth: a review. Phys Life Rev 18:66–97
10. Chowell G, Viboud C, Hyman JM, Simonsen L (2015) The Western Africa ebola virus disease epidemic exhibits both global exponential and local polynomial growth rates. PLoS Curr. doi:10.1371/currents.outbreaks.8b55f4bad99ac5c5db3663e916803261
11. Chowell G, Viboud C, Simonsen L, Moghadas S (2016) Characterizing the reproduction number of epidemics with early sub-exponential growth dynamics. ArXiv preprint arXiv:1603.01216
12. Chretien JP, Riley S, George DB (2015) Mathematical modeling of the West Africa Ebola epidemic. eLife 4:e09186
13. Colgate SA, Stanley EA, Hyman JM, Layne SP, Qualls C (1989) Risk behavior-based model of the cubic growth of acquired immunodeficiency syndrome in the United States. Proc Nat Acad Sci USA 86(12):4793–4797
14. Dureau J, Kalogeropoulos K, Baguelin M (2013) Capturing the time-varying drivers of an epidemic using stochastic dynamical systems. Biostatistics 14(3):541–555
15. Engl H, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer Academic, Dordecht
16. Finkenstädt BF, Grenfell BT (2000) Time series modelling of childhood diseases: a dynamical systems approach. J R Stat Soc Ser C (Appl Stat) 49(2):187–205
17. Hadeler KP (2011) Parameter identification in epidemic models. Math Biosci 229(2):185–189
18. Kiskowski MA (2014) A three-scale network model for the early growth dynamics of 2014 West Africa Ebola epidemic. PLOS Curr. doi:10.1371/currents.outbreaks.c6efe8274dc55274f05cbcb62bbe6070
19. Lange A (2016) Reconstruction of disease transmission rates: applications to measles, dengue, and influenza. J Theor Biol 400:138–153
20. Lekone PE, Finkenstädt BF (2006) Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62(4):1170–1177
21. Lewnard JA, Ndeffo Mbah ML, Alfaro-Murillo JA, Altice FL, Bawo L, Nyenswah TG, Galvani AP (2014) Dynamics and control of Ebola virus transmission in Montserrado, Liberia: a mathematical modelling analysis. Lancet Infect Dis 14(12):1189–1195
22. Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, Gopalakrishna G, Chew SK, Tan CC, Samore MH et al (2003) Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627):1966–1970
23. Meltzer MI, Santibanez S, Fischer LS, Merlin TL, Adhikari BB, Atkins CY, Campbell C, Fung IC, Gambhir M, Gift T et al (2016) Modeling in real time during the Ebola response. MMWR Suppl 65(3):85–89
24. Merler S, Ajelli M, Fumanelli L, Gomes MF, Piontti AP, Rossi L, Chao DL, Longini IM Jr, Halloran ME, Vespignani A (2015) Spatiotemporal spread of the 2014 outbreak of Ebola virus disease in Liberia and the effectiveness of non-pharmaceutical interventions: a computational modelling analysis. Lancet Infect Dis 15(2):204–211
25. Morozov VA (1984) Methods for solving incorrectly posed problems. Springer, Berlin
26. Newman MEJ (2002) Spread of epidemic disease on networks. Phys Rev E 66(1):016128
27. Pollicott M, Wang H, Weiss H (2012) Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem. J Biol Dyn 6(2):509–523
28. Ponciano JM, Capistrán MA (2011) First principles modeling of nonlinear incidence rates in seasonal epidemics. PLoS Comput Biol 7(2):e1001079
29. Rivers CM, Lofgren ET, Marathe M, Eubank S, Lewis BL (2014) Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia. ArXiv preprint arXiv:1409.4607
30. Szendroi B, Csnyi G (2004) Polynomial epidemics and clustering in contact networks. Proc R Soc Lond B Biol Sci 271(Suppl 5):S364–S366
31. Szusz EK, Garrison LP, Bauch CT (2010) A review of data needed to parameterize a dynamic model of measles in developing countries. BMC Res Notes 3(1):1
32. Taylor BP, Dushoff J, Weitz JS (2016) Stochasticity and the limits to confidence when estimating r_0 of Ebola and other emerging infectious diseases. ArXiv preprint arXiv:1601.06829
33. Viboud C, Simonsen L, Chowell G (2016) A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks. Epidemics 15:27–37
34. World Health Organization, Statement on the 1st meeting of the IHR Emergency Committee on the 2014 Ebola outbreak in West Africa, retrieved 6/10/15. http://www.who.int/mediacentre/news/statements/2014/ebola-20140808/en/
35. World Health Organization, Ebola Situation Report—30 March 2016, retrieved 6/01/16. http://apps.who.int/ebola/current-situation/ebola-situation-report-30-march-2016
36. Xia Y, Bjørnstad ON, Grenfell BT (2004) Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics. Am Nat 164(2):267–281