Imperfect Vaccine Aggravates the Long-Standing Dilemma of Voluntary Vaccination

Achieving widespread population immunity by voluntary vaccination poses a major challenge for public health administration and practice. The situation is complicated even more by imperfect vaccines. How the vaccine efficacy affects individuals' vaccination behavior has yet to be fully answered. To address this issue, we combine a simple yet effective game theoretic model of vaccination behavior with an epidemiological process. Our analysis shows that, in a population of self-interested individuals, there exists an overshooting of vaccine uptake levels as the effectiveness of vaccination increases. Moreover, when the basic reproductive number, , exceeds a certain threshold, all individuals opt for vaccination for an intermediate region of vaccine efficacy. We further show that increasing effectiveness of vaccination always increases the number of effectively vaccinated individuals and therefore attenuates the epidemic strain. The results suggest that ‘number is traded for efficiency’: although increases in vaccination effectiveness lead to uptake drops due to free-riding effects, the impact of the epidemic can be better mitigated.

[1]  G. Szabó,et al.  Evolutionary prisoner's dilemma game on a square lattice , 1997, cond-mat/9710096.

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

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

[4]  François Taddei,et al.  The Durability of Public Goods Changes the Dynamics and Nature of Social Dilemmas , 2007, PloS one.

[5]  M. Perc.  Coherence resonance in a spatial prisoner's dilemma game , 2006 .

[6]  Yamir Moreno,et al.  Complex Cooperative Networks from Evolutionary Preferential Attachment , 2008, PloS one.

[7]  Matjaz Perc,et al.  Coveting thy neighbors fitness as a means to resolve social dilemmas , 2011, Journal of theoretical biology.

[8]  M. Nowak,et al.  Stochastic dynamics of invasion and fixation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[10]  A. Hinman,et al.  State of immunity: The politics of vaccination in twentieth-century America , 2007 .

[11]  Frederick Chen.  A Susceptible-infected Epidemic Model with Voluntary Vaccinations , 2006, Journal of mathematical biology.

[12]  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.

[13]  Long Wang,et al.  Evolution of Cooperation on Stochastic Dynamical Networks , 2010, PloS one.

[14]  L. Blume.  The Statistical Mechanics of Strategic Interaction , 1993 .

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

[16]  Timothy C. Reluga,et al.  A general approach for population games with application to vaccination. , 2011, Mathematical biosciences.

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

[18]  Zhen Wang,et al.  Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game , 2010, PloS one.

[19]  Attila Szolnoki,et al.  Phase Diagrams for the Spatial Public Goods Game with Pool-Punishment , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[21]  C. Bauch,et al.  Rapid Emergence of Free-Riding Behavior in New Pediatric Immunization Programs , 2010, PloS one.

[22]  C. Sudfeld,et al.  Effectiveness of measles vaccination and vitamin A treatment , 2010, International journal of epidemiology.

[23]  Martin A. Nowak,et al.  Chromodynamics of Cooperation in Finite Populations , 2007, PloS one.

[24]  Attila Szolnoki,et al.  Reward and cooperation in the spatial public goods game , 2010, ArXiv.

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

[26]  Ana Perisic,et al.  Social Contact Networks and Disease Eradicability under Voluntary Vaccination , 2009, PLoS Comput. Biol..

[27]  Yi Tao,et al.  Cooperation and Stability through Periodic Impulses , 2010, PloS one.

[28]  Franz J. Weissing,et al.  Self-Interest versus Group-Interest in Antiviral Control , 2008, PloS one.

[29]  Long Wang,et al.  Universality of weak selection. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  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.

[31]  Attila Szolnoki,et al.  Topology-independent impact of noise on cooperation in spatial public goods games. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[33]  Arne Traulsen,et al.  Human strategy updating in evolutionary games , 2010, Proceedings of the National Academy of Sciences.

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

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

[36]  W. Rudin.  Principles of mathematical analysis , 1964 .

[37]  S. Hoffman.  Malaria vaccine development: a multi-immune response approach , 1996 .

[38]  Lauren Ancel Meyers,et al.  Erratic Flu Vaccination Emerges from Short-Sighted Behavior in Contact Networks , 2011, PLoS Comput. Biol..

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

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

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