Disease Control through Voluntary Vaccination Decisions Based on the Smoothed Best Response

We investigate game-theory based decisions on vaccination uptake and its effects on the spread of an epidemic with nonlinear incidence rate. It is assumed that each individual's decision approximates his/her best response (called smoothed best response) in that this person chooses to take the vaccine based on its cost-benefit analysis. The basic reproduction number of the resultant epidemic model is calculated and used to characterize the existence and stability of the disease-free and endemic equilibria of the model. The effects on the spread and control of the epidemic are revealed in terms of the sensitivity of the response to changes in costs and benefits, in the “cost” of the vaccination, and in the proportion of susceptible individuals who are faced with the decision of whether or not to be vaccinated per unit time. The effects of the best response decision rule are also analyzed and compared to those of the smoothed best response. Our study shows that, when there is a perceived cost to take the vaccine, the smoothed best response is more effective in controlling the epidemic. However, when this cost is 0, the best response is the more efficient control.

[1]  John J. Grefenstette,et al.  A game dynamic model for vaccine skeptics and vaccine believers: measles as an example. , 2012, Journal of theoretical biology.

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

[3]  Ju Lu,et al.  Double-edged sword: The effect of exergaming on other forms of exercise; a randomized controlled trial using the self-categorization theory , 2016, Comput. Hum. Behav..

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

[5]  R. Cressman,et al.  Migration Dynamics for the Ideal Free Distribution , 2006, The American Naturalist.

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

[7]  S. Connolly,et al.  Economics of the Public Sector , 1999 .

[8]  Xingfu Zou,et al.  Flu epidemics: a two-strain flu model with a single vaccination , 2011 .

[9]  Xuebin Chi,et al.  The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission , 2002 .

[10]  Emily K. Szusz,et al.  Scheduling of measles vaccination in low-income countries: projections of a dynamic model. , 2009, Vaccine.

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

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

[13]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[14]  P. Verhulst.  Recherches mathématiques sur la loi d’accroissement de la population , 2022, Nouveaux mémoires de l'Académie royale des sciences et belles-lettres de Bruxelles.

[15]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

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

[17]  Ross Cressman,et al.  Evolution of mobility in predator-prey systems , 2014 .

[18]  Julien Arino,et al.  A model for influenza with vaccination and antiviral treatment. , 2008, Journal of theoretical biology.

[19]  Ross Cressman,et al.  The effects of opportunistic and intentional predators on the herding behavior of prey. , 2011, Ecology.

[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]  Lawrence E. Barker,et al.  Logit Models From Economics and Other Fields , 2005, Technometrics.

[22]  Frederick Chen,et al.  A mathematical analysis of public avoidance behavior during epidemics using game theory. , 2012, Journal of theoretical biology.

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

[24]  R. Cressman.  Evolutionary Dynamics and Extensive Form Games , 2003 .

[25]  R. Ruth,et al.  Stability of dynamical systems , 1988 .

[26]  David J D Earn,et al.  Population dynamics of live-attenuated virus vaccines. , 2010, Theoretical population biology.

[27]  S. Merler,et al.  Risk perception and effectiveness of uncoordinated behavioral responses in an emerging epidemic. , 2012, Mathematical biosciences.

[28]  Feng Fu,et al.  Rational behavior is a ‘double-edged sword’ when considering voluntary vaccination , 2012 .

[29]  Julien Arino,et al.  Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation , 2003, SIAM J. Appl. Math..

[30]  Chris T Bauch,et al.  A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks , 2009, BMC infectious diseases.

[31]  Luiz Henrique Alves Monteiro,et al.  A vaccination game based on public health actions and personal decisions , 2011 .