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Statistical challenges and opportunities in modelling coupled behaviour-disease dynamics of vaccine refusal
Last modified: 2018-05-21
Abstract
Vaccine refusal has proven to be a persistent foe in efforts to protect populations from infectious diseases. Â One hypothesis about its origin posits a coupling between vaccinating behaviour and disease transmission: when infection prevalence is sufficiently low, individuals become complacent and vaccinating becomes less desirable, causing a decline in vaccine coverage and resurgence of the disease. Â This dynamic is being explored in a growing number of mathematical models. Â Here, I present a differential equation model of coupled behaviour-disease dynamics for vaccine-preventable paediatric infections, and I discuss previous research that has applied various statistical methodologies to parameterize and validate the model. Â I will show how methodologies such as model selection analysis and statistical learning, in conjunction with mechanistic modelling, can be used to test for the presence of phenomena related to coupled behaviour-disease dynamics during episodes of vaccine refusal. Â These phenomena include social learning and imitation, social norms, criticality, and coupling between vaccinating behaviour and disease prevalence. Â Some of these methodologies exploit new data sources such as online social media. I conclude that the study and modelling of vaccine refusal can greatly benefit from using mechanistic models informed by both traditional and state-of-the-art statistical methodologies.
References
\begin{thebibliography}{10}
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\bibitem{barlow2014modelling}L.A. Barlow, J.~Cecile, C.T. Bauch, and M.~Anand.\newblock Modelling interactions between forest pest invasions and human decisions regarding firewood transport restrictions.\newblock {\em PLoS One}, 9(4):e90511, 2014.
\bibitem{bauch_2005}C.~T. Bauch.\newblock Imitation dynamics predict vaccinating behaviour.\newblock {\em Proc. R. Soc. Lond. B.}, 272:1669--1675, 2005.
\bibitem{bauch_2012}C.~T. Bauch and S.~Bhattacharyya.\newblock Evolutionary game theory and social learning can determine how vaccine scares unfold.\newblock {\em {PLoS} Comp Biol}, 8(4):e1002452, 2012.
\bibitem{bauch2004vaccination}C.T. Bauch and D.J.D. Earn.\newblock Vaccination and the theory of games.\newblock {\em Proc. Natl. Acad. Sci. USA}, 101(36):13391--13394, 2004.
\bibitem{bauch2013social}C.T. Bauch and A.P. Galvani.\newblock Social factors in epidemiology.\newblock {\em Science}, 342:47--49, 2013.
\bibitem{bauch2003group}C.T. Bauch, A.P. Galvani, and D.J.D. Earn.\newblock Group interest versus self-interest in smallpox vaccination policy.\newblock {\em Proc. Natl. Acad. Sci. USA}, 100(18):10564--67, 2003.
\bibitem{bauch2016early}C.T. Bauch, R.~Sigdel, J.~Pharaon, and M.~Anand.\newblock Early warning signals of regime shifts in coupled human--environment systems.\newblock {\em Proc. Natl. Acad. Sci. USA}, 113:14560--67, 2016.
\bibitem{bonanni_1998}P.~Bonanni.\newblock Demographic impact of vaccination: a review.\newblock {\em Vaccine}, 17:S120--S125, 1998.
\bibitem{brien2012determinants}S.~Brien, J.C. Kwong, and D.L. Buckeridge.\newblock The determinants of 2009 pandemic {A/H1N1} influenza vaccination: a systematic review.\newblock {\em Vaccine}, 30(7):1255--1264, 2012.
\bibitem{brito_1991}D.L. Brito and E.~Sheshinski.\newblock Externalities and compulsory vaccinations.\newblock {\em Journal of Public Economics}, 45:69--90, 1991.
\bibitem{burnham2003model}K.P. Burnham and D.R. Anderson.\newblock {\em Model selection and multimodel inference: a practical information-theoretic approach}.\newblock Springer Science \& Business Media, 2003.
\bibitem{canning_2005}H.S. Canning et~al.\newblock Health care worker beliefs about influenza vaccine and reasons for non-vaccination: a cross-sectional survey.\newblock {\em Journal of Clinical Nursing}, 14(8):922--925, 2005.
\bibitem{capasso1978generalization}V.~Capasso and G.~Serio.\newblock A generalization of the {Kermack-McKendrick} deterministic epidemic model.\newblock {\em Mathematical Biosciences}, 42(1-2):43--61, 1978.
\bibitem{chapman_1999}G.~Chapman and E.~Coups.\newblock Predictors of influenza vaccine acceptance among healthy adults.\newblock {\em Preventive Medicine}, 29(4):249--262, 1999.
\bibitem{de2008feasibility}C.A. De~Quadros, J.K. Andrus, et~al.\newblock Feasibility of global measles eradication after interruption of transmission in the americas.\newblock {\em Expert review of vaccines}, 7(3):355--362, 2008.
\bibitem{d2011impact}A.~d'Onofrio, P.~Manfredi, and P.~Poletti.\newblock The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach.\newblock {\em J. Theor. Biol}, 273:63--71, 2011.
\bibitem{d2007vaccinating}A.~d'Onofrio, P.~Manfredi, and E.~Salinelli.\newblock Vaccinating behaviour, information, and the dynamics of sir vaccine preventable diseases.\newblock {\em Theor. Pop. Biol.}, 71(3):301--317, 2007.
\bibitem{d2009information}Alberto d'Onofrio and Piero Manfredi.\newblock Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases.\newblock {\em Journal of Theoretical Biology}, 256(3):473--478, 2009.
\bibitem{fenner_1988}F.~Fenner, D.~A. Henderson, I.~Arita, et~al.\newblock Smallpox and its eradication.\newblock World Health Organization, Geneva, 1988.
\bibitem{fine_1986}P.E.M. Fine and J.A. Clarkson.\newblock Individual versus public priorities in the determination of optimal vaccination policies.\newblock {\em Am. J. Epidemiol.}, 124:1012--1020, 1986.
\bibitem{funk2015nine}S.~Funk, S.~Bansal, C.T. Bauch, et~al.\newblock Nine challenges in incorporating the dynamics of behaviour in infectious diseases models.\newblock {\em Epidemics}, 10:21--25, 2015.
\bibitem{funk2010modelling}S.~Funk, M.~Salath{\'e}, and V.A.A. Jansen.\newblock Modelling the influence of human behaviour on the spread of infectious diseases: a review.\newblock {\em J. R. Soc. Interface}, page rsif20100142, 2010.
\bibitem{gilbert2014probabilistic}J.A. Gilbert, L.A. Meyers, A.P. Galvani, et~al.\newblock Probabilistic uncertainty analysis of epidemiological modeling to guide public health intervention policy.\newblock {\em Epidemics}, 6:37--45, 2014.
\bibitem{goldstein1996effect}K.P. Goldstein, T.J. Philipson, H.~Joo, and R.S. Daum.\newblock The effect of epidemic measles on immunization rates.\newblock {\em JAMA}, 276(1):56--58, 1996.
\bibitem{gross_2006}T.~Gross, C.J.~Dommar D'Lima, and B.~Blasius.\newblock Epidemic dynamics on an adaptive network.\newblock {\em Phys. Rev. Lett.}, 96(20):208701, 2006.
\bibitem{hadeler1995core}K.P. Hadeler and C.~Castillo-Ch{\'a}vez.\newblock A core group model for disease transmission.\newblock {\em Mathematical biosciences}, 128(1-2):41--55, 1995.
\bibitem{halsey2015measles}N.A. Halsey and D.A. Salmon.\newblock Measles at {Disneyland}, a problem for all ages.\newblock {\em Annals of internal medicine}, 162(9):655--656, 2015.
\bibitem{he2009plug}D.~He, E.L. Ionides, and A.A. King.\newblock Plug-and-play inference for disease dynamics: measles in large and small populations as a case study.\newblock {\em J. Roy. Soc. Interface}, 2009.
\bibitem{henderson2016alternative}K.A. Henderson, C.T. Bauch, and M.~Anand.\newblock Alternative stable states and the sustainability of forests, grasslands, and agriculture.\newblock {\em Proc. Natl. Acad. Sci. USA}, 113(51):14552--14559, 2016.
\bibitem{hethcote_2000a}H.W. Hethcote.\newblock The mathematics of infectious diseases.\newblock {\em SIAM Review}, 42(4):599--653, 2000.
\bibitem{innes2013impact}C.~Innes, M.~Anand, and C.T. Bauch.\newblock The impact of human-environment interactions on the stability of forest-grassland mosaic ecosystems.\newblock {\em Scientific reports}, 3:2689, 2013.
\bibitem{jegede2007led}A.S. Jegede.\newblock What led to the {Nigerian} boycott of the polio vaccination campaign?\newblock {\em PLoS Medicine}, 4(3):e73, 2007.
\bibitem{liu2007complexity}J.~Liu, T.~Dietz, S.R. Carpenter, et~al.\newblock Complexity of coupled human and natural systems.\newblock {\em science}, 317(5844):1513--1516, 2007.
\bibitem{manfredi2013modeling}P.~Manfredi and A.~D'Onofrio.\newblock {\em Modeling the interplay between human behavior and the spread of infectious diseases}.\newblock Springer Science \& Business Media, 2013.
\bibitem{murray1996global}C.J.L. Murray, A.D. Lopez, World~Health Organization, et~al.\newblock The global burden of disease: a comprehensive assessment of mortality and disability from diseases, injuries, and risk factors in 1990 and projected to 2020: summary.\newblock {\em Global burden of disease and injury series}, 1996.
\bibitem{oraby2014influence}T.~Oraby, V.~Thampi, and C.T. Bauch.\newblock The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases.\newblock {\em Proc. R. Soc. B}, 281:20133172, 2014.
\bibitem{pananos2017critical}A.D. Pananos, T.M. Bury, C.~Wang, et~al.\newblock Critical dynamics in population vaccinating behavior.\newblock {\em Proc. Natl. Acad. Sci. {USA}}, page 201704093, 2017.
\bibitem{salathe2012digital}M.~Salathe, L.~Bengtsson, T.J. Bodnar, et~al.\newblock Digital epidemiology.\newblock {\em PLoS Computational Biology}, 8(7):e1002616, 2012.
\bibitem{salathe2011assessing}M.~Salath{\'e} and S.~Khandelwal.\newblock Assessing vaccination sentiments with online social media:Â implications for infectious disease dynamics and control.\newblock {\em PLoS computational biology}, 7(10):e1002199, 2011.
\bibitem{scheffer2009early}M.~Scheffer, J.~Bascompte, W.A. Brock, et~al.\newblock Early-warning signals for critical transitions.\newblock {\em Nature}, 461(7260):53, 2009.
\bibitem{scholkopf2002learning}B.~Sch{\"o}lkopf and A.J. Smola.\newblock {\em Learning with kernels: support vector machines, regularization, optimization, and beyond}.\newblock MIT press, 2002.
\bibitem{verelst2016behavioural}F.~Verelst, L.~Willem, and P.~Beutels.\newblock Behavioural change models for infectious disease transmission: a systematic review (2010--2015).\newblock {\em Journal of The Royal Society Interface}, 13(125):20160820, 2016.
\bibitem{verger2015vaccine}P.~Verger et~al.\newblock Vaccine hesitancy among general practitioners and its determinants during controversies: a national cross-sectional survey in {France}.\newblock {\em EBioMedicine}, 2(8):891--897, 2015.
\bibitem{wang2015coupled}Z.~Wang, M.A. Andrews, Z.~Wu, et~al.\newblock Coupled disease--behavior dynamics on complex networks: A review.\newblock {\em Physics of life reviews}, 15:1--29, 2015.
\bibitem{wang2016statistical}Z.~Wang, C.T. Bauch, S.~Bhattacharyya, et~al.\newblock Statistical physics of vaccination.\newblock {\em Physics Reports}, 664:1--113, 2016.
\end{thebibliography}
\bibitem{anderson_1991a}R.~M. Anderson and R.~M. May.\newblock {\em Infectious Diseases of Humans}.\newblock Oxford University Press, Oxford, 1991.
\bibitem{barlow2014modelling}L.A. Barlow, J.~Cecile, C.T. Bauch, and M.~Anand.\newblock Modelling interactions between forest pest invasions and human decisions regarding firewood transport restrictions.\newblock {\em PLoS One}, 9(4):e90511, 2014.
\bibitem{bauch_2005}C.~T. Bauch.\newblock Imitation dynamics predict vaccinating behaviour.\newblock {\em Proc. R. Soc. Lond. B.}, 272:1669--1675, 2005.
\bibitem{bauch_2012}C.~T. Bauch and S.~Bhattacharyya.\newblock Evolutionary game theory and social learning can determine how vaccine scares unfold.\newblock {\em {PLoS} Comp Biol}, 8(4):e1002452, 2012.
\bibitem{bauch2004vaccination}C.T. Bauch and D.J.D. Earn.\newblock Vaccination and the theory of games.\newblock {\em Proc. Natl. Acad. Sci. USA}, 101(36):13391--13394, 2004.
\bibitem{bauch2013social}C.T. Bauch and A.P. Galvani.\newblock Social factors in epidemiology.\newblock {\em Science}, 342:47--49, 2013.
\bibitem{bauch2003group}C.T. Bauch, A.P. Galvani, and D.J.D. Earn.\newblock Group interest versus self-interest in smallpox vaccination policy.\newblock {\em Proc. Natl. Acad. Sci. USA}, 100(18):10564--67, 2003.
\bibitem{bauch2016early}C.T. Bauch, R.~Sigdel, J.~Pharaon, and M.~Anand.\newblock Early warning signals of regime shifts in coupled human--environment systems.\newblock {\em Proc. Natl. Acad. Sci. USA}, 113:14560--67, 2016.
\bibitem{bonanni_1998}P.~Bonanni.\newblock Demographic impact of vaccination: a review.\newblock {\em Vaccine}, 17:S120--S125, 1998.
\bibitem{brien2012determinants}S.~Brien, J.C. Kwong, and D.L. Buckeridge.\newblock The determinants of 2009 pandemic {A/H1N1} influenza vaccination: a systematic review.\newblock {\em Vaccine}, 30(7):1255--1264, 2012.
\bibitem{brito_1991}D.L. Brito and E.~Sheshinski.\newblock Externalities and compulsory vaccinations.\newblock {\em Journal of Public Economics}, 45:69--90, 1991.
\bibitem{burnham2003model}K.P. Burnham and D.R. Anderson.\newblock {\em Model selection and multimodel inference: a practical information-theoretic approach}.\newblock Springer Science \& Business Media, 2003.
\bibitem{canning_2005}H.S. Canning et~al.\newblock Health care worker beliefs about influenza vaccine and reasons for non-vaccination: a cross-sectional survey.\newblock {\em Journal of Clinical Nursing}, 14(8):922--925, 2005.
\bibitem{capasso1978generalization}V.~Capasso and G.~Serio.\newblock A generalization of the {Kermack-McKendrick} deterministic epidemic model.\newblock {\em Mathematical Biosciences}, 42(1-2):43--61, 1978.
\bibitem{chapman_1999}G.~Chapman and E.~Coups.\newblock Predictors of influenza vaccine acceptance among healthy adults.\newblock {\em Preventive Medicine}, 29(4):249--262, 1999.
\bibitem{de2008feasibility}C.A. De~Quadros, J.K. Andrus, et~al.\newblock Feasibility of global measles eradication after interruption of transmission in the americas.\newblock {\em Expert review of vaccines}, 7(3):355--362, 2008.
\bibitem{d2011impact}A.~d'Onofrio, P.~Manfredi, and P.~Poletti.\newblock The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach.\newblock {\em J. Theor. Biol}, 273:63--71, 2011.
\bibitem{d2007vaccinating}A.~d'Onofrio, P.~Manfredi, and E.~Salinelli.\newblock Vaccinating behaviour, information, and the dynamics of sir vaccine preventable diseases.\newblock {\em Theor. Pop. Biol.}, 71(3):301--317, 2007.
\bibitem{d2009information}Alberto d'Onofrio and Piero Manfredi.\newblock Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases.\newblock {\em Journal of Theoretical Biology}, 256(3):473--478, 2009.
\bibitem{fenner_1988}F.~Fenner, D.~A. Henderson, I.~Arita, et~al.\newblock Smallpox and its eradication.\newblock World Health Organization, Geneva, 1988.
\bibitem{fine_1986}P.E.M. Fine and J.A. Clarkson.\newblock Individual versus public priorities in the determination of optimal vaccination policies.\newblock {\em Am. J. Epidemiol.}, 124:1012--1020, 1986.
\bibitem{funk2015nine}S.~Funk, S.~Bansal, C.T. Bauch, et~al.\newblock Nine challenges in incorporating the dynamics of behaviour in infectious diseases models.\newblock {\em Epidemics}, 10:21--25, 2015.
\bibitem{funk2010modelling}S.~Funk, M.~Salath{\'e}, and V.A.A. Jansen.\newblock Modelling the influence of human behaviour on the spread of infectious diseases: a review.\newblock {\em J. R. Soc. Interface}, page rsif20100142, 2010.
\bibitem{gilbert2014probabilistic}J.A. Gilbert, L.A. Meyers, A.P. Galvani, et~al.\newblock Probabilistic uncertainty analysis of epidemiological modeling to guide public health intervention policy.\newblock {\em Epidemics}, 6:37--45, 2014.
\bibitem{goldstein1996effect}K.P. Goldstein, T.J. Philipson, H.~Joo, and R.S. Daum.\newblock The effect of epidemic measles on immunization rates.\newblock {\em JAMA}, 276(1):56--58, 1996.
\bibitem{gross_2006}T.~Gross, C.J.~Dommar D'Lima, and B.~Blasius.\newblock Epidemic dynamics on an adaptive network.\newblock {\em Phys. Rev. Lett.}, 96(20):208701, 2006.
\bibitem{hadeler1995core}K.P. Hadeler and C.~Castillo-Ch{\'a}vez.\newblock A core group model for disease transmission.\newblock {\em Mathematical biosciences}, 128(1-2):41--55, 1995.
\bibitem{halsey2015measles}N.A. Halsey and D.A. Salmon.\newblock Measles at {Disneyland}, a problem for all ages.\newblock {\em Annals of internal medicine}, 162(9):655--656, 2015.
\bibitem{he2009plug}D.~He, E.L. Ionides, and A.A. King.\newblock Plug-and-play inference for disease dynamics: measles in large and small populations as a case study.\newblock {\em J. Roy. Soc. Interface}, 2009.
\bibitem{henderson2016alternative}K.A. Henderson, C.T. Bauch, and M.~Anand.\newblock Alternative stable states and the sustainability of forests, grasslands, and agriculture.\newblock {\em Proc. Natl. Acad. Sci. USA}, 113(51):14552--14559, 2016.
\bibitem{hethcote_2000a}H.W. Hethcote.\newblock The mathematics of infectious diseases.\newblock {\em SIAM Review}, 42(4):599--653, 2000.
\bibitem{innes2013impact}C.~Innes, M.~Anand, and C.T. Bauch.\newblock The impact of human-environment interactions on the stability of forest-grassland mosaic ecosystems.\newblock {\em Scientific reports}, 3:2689, 2013.
\bibitem{jegede2007led}A.S. Jegede.\newblock What led to the {Nigerian} boycott of the polio vaccination campaign?\newblock {\em PLoS Medicine}, 4(3):e73, 2007.
\bibitem{liu2007complexity}J.~Liu, T.~Dietz, S.R. Carpenter, et~al.\newblock Complexity of coupled human and natural systems.\newblock {\em science}, 317(5844):1513--1516, 2007.
\bibitem{manfredi2013modeling}P.~Manfredi and A.~D'Onofrio.\newblock {\em Modeling the interplay between human behavior and the spread of infectious diseases}.\newblock Springer Science \& Business Media, 2013.
\bibitem{murray1996global}C.J.L. Murray, A.D. Lopez, World~Health Organization, et~al.\newblock The global burden of disease: a comprehensive assessment of mortality and disability from diseases, injuries, and risk factors in 1990 and projected to 2020: summary.\newblock {\em Global burden of disease and injury series}, 1996.
\bibitem{oraby2014influence}T.~Oraby, V.~Thampi, and C.T. Bauch.\newblock The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases.\newblock {\em Proc. R. Soc. B}, 281:20133172, 2014.
\bibitem{pananos2017critical}A.D. Pananos, T.M. Bury, C.~Wang, et~al.\newblock Critical dynamics in population vaccinating behavior.\newblock {\em Proc. Natl. Acad. Sci. {USA}}, page 201704093, 2017.
\bibitem{salathe2012digital}M.~Salathe, L.~Bengtsson, T.J. Bodnar, et~al.\newblock Digital epidemiology.\newblock {\em PLoS Computational Biology}, 8(7):e1002616, 2012.
\bibitem{salathe2011assessing}M.~Salath{\'e} and S.~Khandelwal.\newblock Assessing vaccination sentiments with online social media:Â implications for infectious disease dynamics and control.\newblock {\em PLoS computational biology}, 7(10):e1002199, 2011.
\bibitem{scheffer2009early}M.~Scheffer, J.~Bascompte, W.A. Brock, et~al.\newblock Early-warning signals for critical transitions.\newblock {\em Nature}, 461(7260):53, 2009.
\bibitem{scholkopf2002learning}B.~Sch{\"o}lkopf and A.J. Smola.\newblock {\em Learning with kernels: support vector machines, regularization, optimization, and beyond}.\newblock MIT press, 2002.
\bibitem{verelst2016behavioural}F.~Verelst, L.~Willem, and P.~Beutels.\newblock Behavioural change models for infectious disease transmission: a systematic review (2010--2015).\newblock {\em Journal of The Royal Society Interface}, 13(125):20160820, 2016.
\bibitem{verger2015vaccine}P.~Verger et~al.\newblock Vaccine hesitancy among general practitioners and its determinants during controversies: a national cross-sectional survey in {France}.\newblock {\em EBioMedicine}, 2(8):891--897, 2015.
\bibitem{wang2015coupled}Z.~Wang, M.A. Andrews, Z.~Wu, et~al.\newblock Coupled disease--behavior dynamics on complex networks: A review.\newblock {\em Physics of life reviews}, 15:1--29, 2015.
\bibitem{wang2016statistical}Z.~Wang, C.T. Bauch, S.~Bhattacharyya, et~al.\newblock Statistical physics of vaccination.\newblock {\em Physics Reports}, 664:1--113, 2016.
\end{thebibliography}
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