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A note on observation processes in epidemic models. (English) Zbl 1435.92081

Summary: Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic susceptible-infected-removed (SIR) model to compare two common assumptions about disease incidence reports: Individuals can report their infection as soon as they become infected or as soon as they recover. We show that incorrect assumptions about the underlying observation processes can bias estimates of the basic reproduction number and lead to overly narrow confidence intervals.

MSC:

92D30 Epidemiology

Software:

epimdr; epimdr2

References:

[1] Anderson, D.; Watson, R., On the spread of a disease with gamma distributed latent and infectious periods, Biometrika, 67, 1, 191-198 (1980) · Zbl 0421.92023 · doi:10.1093/biomet/67.1.191
[2] Bhadra, A.; Ionides, EL; Laneri, K.; Pascual, M.; Bouma, M.; Dhiman, RC, Malaria in Northwest India: data analysis via partially observed stochastic differential equation models driven by Lévy noise, J Am Stat Assoc, 106, 494, 440-451 (2011) · Zbl 1232.62143 · doi:10.1198/jasa.2011.ap10323
[3] Birrell, PJ; Ketsetzis, G.; Gay, NJ; Cooper, BS; Presanis, AM; Harris, RJ; Charlett, A.; Zhang, X-S; White, PJ; Pebody, RG, Bayesian modeling to unmask and predict influenza A/H1N1pdm dynamics in London, Proc Natl Acad Sci, 108, 45, 18238-18243 (2011) · doi:10.1073/pnas.1103002108
[4] Bjørnstad, ON, Epidemics: models and data using R (2018), Berlin: Springer, Berlin · Zbl 1407.92001
[5] Bretó, C.; He, D.; Ionides, EL; King, AA, Time series analysis via mechanistic models, Ann Appl Stat, 3, 1, 319-348 (2009) · Zbl 1160.62080 · doi:10.1214/08-AOAS201
[6] Browne, C.; Gulbudak, H.; Webb, G., Modeling contact tracing in outbreaks with application to Ebola, J Theor Biol, 384, 33-49 (2015) · Zbl 1343.92462 · doi:10.1016/j.jtbi.2015.08.004
[7] Capistrán, MA; Moreles, MA; Lara, B., Parameter estimation of some epidemic models. The case of recurrent epidemics caused by respiratory syncytial virus, Bull Math Biol, 71, 8, 1890 (2009) · Zbl 1179.92036 · doi:10.1007/s11538-009-9429-3
[8] Cauchemez, S.; Ferguson, NM, Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London, J R Soc Interface, 5, 25, 885-897 (2008) · doi:10.1098/rsif.2007.1292
[9] Dean, KR; Krauer, F.; Walløe, L.; Lingjærde, OC; Bramanti, B.; Stenseth, NC; Schmid, BV, Human ectoparasites and the spread of plague in Europe during the second pandemic, Proc Natl Acad Sci, 115, 6, 1304-1309 (2018) · doi:10.1073/pnas.1715640115
[10] Didelot, X.; Whittles, LK; Hall, I., Model-based analysis of an outbreak of bubonic plague in Cairo in 1801, J R Soc Interface, 14, 131, 20170160 (2017) · doi:10.1098/rsif.2017.0160
[11] Elderd, BD; Dukic, VM; Dwyer, G., Uncertainty in predictions of disease spread and public health responses to bioterrorism and emerging diseases, Proc Natl Acad Sci, 103, 42, 15693-15697 (2006) · doi:10.1073/pnas.0600816103
[12] Ferguson, NM; Donnelly, CA; Anderson, RM, The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions, Science, 292, 5519, 1155-1160 (2001) · doi:10.1126/science.1061020
[13] Fine, PE; Clarkson, JA, Measles in England and Wales-I: an analysis of factors underlying seasonal patterns, Int J Epidemiol, 11, 1, 5-14 (1982) · doi:10.1093/ije/11.1.5
[14] Funk, S.; Camacho, A.; Kucharski, AJ; Eggo, RM; Edmunds, WJ, Real-time forecasting of infectious disease dynamics with a stochastic semi-mechanistic model, Epidemics, 22, 56-61 (2018) · doi:10.1016/j.epidem.2016.11.003
[15] Goldstein, E.; Dushoff, J.; Ma, J.; Plotkin, JB; Earn, DJ; Lipsitch, M., Reconstructing influenza incidence by deconvolution of daily mortality time series, Proc Natl Acad Sci, 106, 51, 21825-21829 (2009) · doi:10.1073/pnas.0902958106
[16] González-Parra, G.; Arenas, AJ; Chen-Charpentier, BM, A fractional order epidemic model for the simulation of outbreaks of influenza A (H1N1), Math Methods Appl Sci, 37, 15, 2218-2226 (2014) · Zbl 1300.92099 · doi:10.1002/mma.2968
[17] Harris, JE, Reporting delays and the incidence of AIDS, J Am Stat Assoc, 85, 412, 915-924 (1990) · doi:10.1080/01621459.1990.10474962
[18] He, D.; Dushoff, J.; Day, T.; Ma, J.; Earn, DJ, Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales, Proc R Soc B Biol Sci, 280, 1766, 20131345 (2013) · doi:10.1098/rspb.2013.1345
[19] He, D.; Ionides, EL; King, AA, Plug-and-play inference for disease dynamics: measles in large and small populations as a case study, J R Soc Interface, 7, 43, 271-283 (2009) · doi:10.1098/rsif.2009.0151
[20] Hooker, G.; Ellner, SP; Roditi, LDV; Earn, DJ, Parameterizing state-space models for infectious disease dynamics by generalized profiling: measles in Ontario, J R Soc Interface, 8, 60, 961-974 (2010) · doi:10.1098/rsif.2010.0412
[21] Keeling, M.; Grenfell, BT, Effect of variability in infection period on the persistence and spatial spread of infectious diseases, Math Biosci, 147, 2, 207-226 (1998) · Zbl 0887.92028 · doi:10.1016/S0025-5564(97)00101-6
[22] Kennedy, DA; Dunn, PA; Read, AF, Modeling Marek’s disease virus transmission: a framework for evaluating the impact of farming practices and evolution, Epidemics, 23, 85-95 (2018) · doi:10.1016/j.epidem.2018.01.001
[23] Kermack, WO; McKendrick, AG, A contribution to the mathematical theory of epidemics, Proc R Soc A Math Phys Eng Sci, 115, 772, 700-721 (1927) · JFM 53.0517.01
[24] King, AA; Domenech de Cellès, M.; Magpantay, FM; Rohani, P., Avoidable errors in the modelling of outbreaks of emerging pathogens, with special reference to Ebola, Proc R Soc B Biol Sci, 282, 1806, 20150347 (2015) · doi:10.1098/rspb.2015.0347
[25] Krylova, O.; Earn, DJ, Effects of the infectious period distribution on predicted transitions in childhood disease dynamics, J R Soc Interface, 10, 84, 20130098 (2013) · doi:10.1098/rsif.2013.0098
[26] Lin, Q.; Lin, Z.; Chiu, AP; He, D., Seasonality of influenza A (H7N9) virus in China-fitting simple epidemic models to human cases, PLoS ONE, 11, 3, e0151333 (2016) · doi:10.1371/journal.pone.0151333
[27] Lloyd, AL, Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods, Proc R Soc B Biol Sci, 268, 1470, 985-993 (2001) · doi:10.1098/rspb.2001.1599
[28] Lloyd, AL, Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics, Theor Popul Biol, 60, 1, 59-71 (2001) · doi:10.1006/tpbi.2001.1525
[29] Martinez, PP; King, AA; Yunus, M.; Faruque, A.; Pascual, M., Differential and enhanced response to climate forcing in diarrheal disease due to rotavirus across a megacity of the developing world, Proc Natl Acad Sci, 113, 15, 4092-4097 (2016) · doi:10.1073/pnas.1518977113
[30] Pons-Salort, M.; Grassly, NC, Serotype-specific immunity explains the incidence of diseases caused by human enteroviruses, Science, 361, 6404, 800-803 (2018) · doi:10.1126/science.aat6777
[31] Schenzle, D., An age-structured model of pre-and post-vaccination measles transmission, Math Med Biol A J IMA, 1, 2, 169-191 (1984) · Zbl 0611.92021 · doi:10.1093/imammb/1.2.169
[32] Ster, IC; Singh, BK; Ferguson, NM, Epidemiological inference for partially observed epidemics: the example of the 2001 foot and mouth epidemic in Great Britain, Epidemics, 1, 1, 21-34 (2009) · doi:10.1016/j.epidem.2008.09.001
[33] Wearing, HJ; Rohani, P.; Keeling, MJ, Appropriate models for the management of infectious diseases, PLoS medicine, 2, 7, e174 (2005) · doi:10.1371/journal.pmed.0020174
[34] Webb, G.; Browne, C.; Huo, X.; Seydi, O.; Seydi, M.; Magal, P., A model of the 2014 Ebola epidemic in West Africa with contact tracing, PLoS Curr (2015) · doi:10.1371/currents.outbreaks.846b2a31ef37018b7d1126a9c8adf22a
[35] Xia, Y.; Bjørnstad, ON; Grenfell, BT, Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics, Am Nat, 164, 2, 267-281 (2004) · doi:10.1086/422341
[36] Yang, J-Y; Chen, Y.; Zhang, F-Q, Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model, J Appl Math Comput, 41, 1-2, 99-117 (2013) · Zbl 1300.34118 · doi:10.1007/s12190-012-0597-1
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