Imperfect vaccine and hysteresis

Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.

[1]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[2]  C. Betsch,et al.  On the benefits of explaining herd immunity in vaccine advocacy , 2017, Nature Human Behaviour.

[3]  Jingzhou Liu,et al.  The Impact of Imitation on Vaccination Behavior in Social Contact Networks , 2012, PLoS Comput. Biol..

[4]  P. Fine,et al.  Individual versus public priorities in the determination of optimal vaccination policies. , 1986, American journal of epidemiology.

[5]  Daniel I. S. Rosenbloom,et al.  Imitation dynamics of vaccination behaviour on social networks , 2011, Proceedings of the Royal Society B: Biological Sciences.

[6]  Long Wang,et al.  Imperfect Vaccine Aggravates the Long-Standing Dilemma of Voluntary Vaccination , 2011, PloS one.

[7]  P. Fine,et al.  Reflections on the efficacy of pertussis vaccines. , 1987, Reviews of infectious diseases.

[8]  C. Bauch.  Imitation dynamics predict vaccinating behaviour , 2005, Proceedings of the Royal Society B: Biological Sciences.

[9]  N. Stollenwerk,et al.  Measles Outbreaks in a Population with Declining Vaccine Uptake , 2003, Science.

[10]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[11]  Eduardo Sontag,et al.  Untangling the wires: A strategy to trace functional interactions in signaling and gene networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[12]  C. Bauch,et al.  The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases , 2014, Proceedings of the Royal Society B: Biological Sciences.

[13]  R. Durrett,et al.  The Importance of Being Discrete (and Spatial) , 1994 .

[14]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

[15]  N. Bayley,et al.  Failure , 1890, The Hospital.

[16]  B. Levin,et al.  Population biology, evolution, and infectious disease: convergence and synthesis. , 1999, Science.

[17]  Dawei Zhao,et al.  Statistical physics of vaccination , 2016, ArXiv.

[18]  Samit Bhattacharyya,et al.  Evolutionary Game Theory and Social Learning Can Determine How Vaccine Scares Unfold , 2012, PLoS Comput. Biol..

[19]  C. Bauch,et al.  Social Factors in Epidemiology , 2013, Science.

[20]  Ken Eames,et al.  "Herd immunity": a rough guide. , 2011, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[21]  Sylvain Gandon,et al.  Imperfect vaccines and the evolution of pathogen virulence , 2001, Nature.

[22]  S. Ratzan,et al.  Addressing the vaccine confidence gap , 2011, The Lancet.

[23]  Sanjay Basu,et al.  Integrating epidemiology, psychology, and economics to achieve HPV vaccination targets , 2008, Proceedings of the National Academy of Sciences.

[24]  C. Hauert,et al.  Coevolutionary dynamics: from finite to infinite populations. , 2004, Physical review letters.

[25]  Jan Medlock,et al.  Optimizing the impact of low-efficacy influenza vaccines , 2018, Proceedings of the National Academy of Sciences.

[26]  Till Bärnighausen,et al.  Valuing vaccination , 2014, Proceedings of the National Academy of Sciences.

[27]  B. Nyhan,et al.  Effective Messages in Vaccine Promotion: A Randomized Trial , 2014, Pediatrics.

[28]  K. Nichol,et al.  The efficacy and cost effectiveness of vaccination against influenza among elderly persons living in the community. , 1994, The New England journal of medicine.

[29]  Ram P. Sigdel,et al.  Early warning signals of regime shifts in coupled human–environment systems , 2016, Proceedings of the National Academy of Sciences.

[30]  Alexander W. Cappelen,et al.  Demand for Childhood Vaccination – Insights from Behavioral Economics , 2010 .

[31]  D. Earn,et al.  Group interest versus self-interest in smallpox vaccination policy , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[32]  P. Wollan,et al.  Secondary failure rates of measles vaccines: a metaanalysis of published studies. , 1996, The Pediatric infectious disease journal.

[33]  R. Axelrod,et al.  Evolutionary Dynamics , 2004 .

[34]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[35]  Timothy C. Reluga,et al.  Evolving public perceptions and stability in vaccine uptake. , 2006, Mathematical biosciences.

[36]  M. Roelants,et al.  Outbreak of mumps in a vaccinated child population: a question of vaccine failure? , 2004, Vaccine.

[37]  Timothy C. Reluga,et al.  Long-standing influenza vaccination policy is in accord with individual self-interest but not with the utilitarian optimum , 2007, Proceedings of the National Academy of Sciences.

[38]  Daniel Lévy-Bruhl,et al.  Measles Elimination Efforts and 2008–2011 Outbreak, France , 2013, Emerging infectious diseases.

[39]  Pejman Rohani,et al.  Impact of immunisation on pertussis transmission in England and Wales , 2000, The Lancet.

[40]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[41]  N G Becker,et al.  Waning immunity and its effects on vaccination schedules. , 1994, Mathematical biosciences.

[42]  J. Leask,et al.  The impact of a vaccine scare on parental views, trust and information needs: a qualitative study in Sydney, Australia , 2017, BMC Public Health.

[43]  B. Bloom,et al.  Addressing Vaccine Hesitancy , 2014, Science.

[44]  C. Vincent,et al.  U.K. parents' decision-making about measles-mumps-rubella (MMR) vaccine 10 years after the MMR-autism controversy: a qualitative analysis. , 2012, Vaccine.

[45]  G. Hardin.  The Tragedy of the Commons , 2009 .

[46]  J. Medlock,et al.  Effectiveness of UNAIDS targets and HIV vaccination across 127 countries , 2017, Proceedings of the National Academy of Sciences.

[47]  M. Slifka,et al.  Public fear of vaccination: separating fact from fiction. , 2005, Viral immunology.

[48]  Rod Cross,et al.  On the Foundations of Hysteresis in Economic Systems , 1993, Economics and Philosophy.

[49]  Derek Powell,et al.  Countering antivaccination attitudes , 2015, Proceedings of the National Academy of Sciences.

[50]  C. Bauch,et al.  Critical dynamics in population vaccinating behavior , 2017, Proceedings of the National Academy of Sciences.

[51]  Kala J. Melchiori,et al.  Association of moral values with vaccine hesitancy , 2017, Nature Human Behaviour.

[52]  Mirjam Kretzschmar,et al.  Estimation of measles vaccine efficacy and critical vaccination coverage in a highly vaccinated population , 2010, Journal of The Royal Society Interface.

[53]  R. Chen,et al.  Vaccine risks: real, perceived and unknown. , 1999, Vaccine.

[54]  Sally M. Blower,et al.  Imperfect vaccines and herd immunity to HIV , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[55]  Y. Grad,et al.  Vaccine waning and mumps re-emergence in the United States , 2017, Science Translational Medicine.

[56]  J. Treanor.  Influenza vaccine--outmaneuvering antigenic shift and drift. , 2004, The New England journal of medicine.

[57]  A. McLean.  Vaccination, evolution and changes in the efficacy of vaccines: a theoretical framework , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[58]  Alison P. Galvani,et al.  Free-Riding Behavior in Vaccination Decisions: An Experimental Study , 2014, PloS one.

[59]  Ming Tang,et al.  Suppressing disease spreading by using information diffusion on multiplex networks , 2016, Scientific Reports.

[60]  Feng Fu,et al.  Dueling biological and social contagions , 2017, Scientific Reports.

[61]  H. Larson.  Politics and public trust shape vaccine risk perceptions , 2018, Nature Human Behaviour.

[62]  J. Baker.  The pertussis vaccine controversy in Great Britain, 1974-1986. , 2003, Vaccine.

[63]  Zhi-Xi Wu,et al.  Peer pressure is a double-edged sword in vaccination dynamics , 2013 .

[64]  G. Chapman,et al.  The influence of altruism on influenza vaccination decisions , 2012, Journal of The Royal Society Interface.

[65]  D J Nokes,et al.  Evaluating the cost-effectiveness of vaccination programmes: a dynamic perspective. , 1999, Statistics in medicine.

[66]  Meredith Wadman,et al.  The vaccine wars. , 2017, Science.

[67]  Raffaele Vardavas,et al.  Can Influenza Epidemics Be Prevented by Voluntary Vaccination? , 2007, PLoS Comput. Biol..

[68]  S. Cleaveland,et al.  Metapopulation dynamics of rabies and the efficacy of vaccination , 2011, Proceedings of the Royal Society B: Biological Sciences.

[69]  J. Leask,et al.  The MMR vaccination and autism controversy in United Kingdom 1998-2005: inevitable community outrage or a failure of risk communication? , 2006, Vaccine.

[70]  E. Miller,et al.  The epidemiology of pertussis in England and Wales. , 1992, Communicable disease report. CDR review.

[71]  Michael Doebeli,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2004, Nature.

[72]  John S Brownstein,et al.  Substandard vaccination compliance and the 2015 measles outbreak. , 2015, JAMA pediatrics.

[73]  D. Earn,et al.  Vaccination and the theory of games. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[74]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .