Abstract
Game theory is the process of modeling strategic interactions between two or more players in a situation containing set rules and outcomes. Game theory is used in many disciplines, but we are interested in introducing here its application to infectious diseases. Vaccination against all childhood diseases poses an interesting dilemma to the parents: if enough children in the population are vaccinated, then their child may be protected and taking the risk and the potential side effects of vaccination might be unnecessary. Thus, every parent must answer the question whether to vaccinate or not their child. Thus, situation can be studied and analyzed with game theory. Because the decision depends on the number of infected/recovered and vaccinated children in the population, the decision depends on time. This leads to application of evolutionary game theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Bauch, Imitation dynamics predict vaccinating behaviour. Proc. R. Soc. B 272, 1669–1675 (2005)
C. Bauch, D. Earn, Vaccination and the theory of games. Proc. Natl Acad. Sci. USA 101, 13391–13394 (2004)
CDC, National Center for Immunization and Respiratory Diseases (NCIRD)
Centers for Disease Control and Prevention, CDC Health Information for International Travel 2014 (Oxford University Press, New York, 2014)
D. Cornforth, T. Reluga, E. Shim, C. Bauch, A. Galvani, L. Meyers, Erratic flu vaccination emerges from short-sighted behaviour in contact networks. Plos Comput. Biol. 7, e1001062 (2011)
R. Cressman, Evolutionary Dynamics and Extensive Form Games (MIT Press, Cambridge, MA, 2003)
A. d’Onofrio, P. Manfredi, Vaccine demand driven by vaccine side effects: dynamic implications for sir diseases. J. Theor. Biol. 264, 237–252 (2010)
A. d’Onofrio, P. Manfredi, P. Poletti, The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach. J. Theor. Biol. 273, 63–71 (2011)
P. Fine, J. Clarkson, Individual versus public priorities in the determination of optimal vaccination policies. Am. J. Epidemiol. 124, 1012–1020 (1986)
F. Fu, D. Rosenbloom, L. Wang, M. Nowak, Imitation dynamics of vaccination behaviour on social networks. Proc. R. Soc. B 278, 42–49 (2011)
M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics. Applied Mathematics Monographs CNR, vol. 7 (Giadini Editorie Stampatori, Pisa, 1994)
P. Magal, Compact attractors for time-periodic age-structured population models. Electron. J. Differ. Equ. 2001, 1–35 (2001)
P. Magal, C.C. McCluskey, G.F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model. Appl. Anal. 89, 1109–1140 (2010)
C. Metcalf, J. Lessler, P. Klepac, F. Cutts, B. Grenfell, Impact of birth rate, seasonality and transmission rate on minimum levels of coverage needed for rubella vaccination. Epidemiol. Infect. 140, 2290–2301 (2012)
T. Reluga, A. Galvani, A general approach for population games with application to vaccination. Math. Biosci. 230, 67–78 (2011)
E. Shim, G. Chapman, A. Galvani, Decision making with regard to antiviral intervention during an influenza pandemic. Med. Decis. Making 30, E64–81 (2010)
E. Shim, J. Grefenstette, S. Albert, B. Cakouros, D. Burke, A game dynamic model for vaccine skeptics and vaccine believers: measles as an example. J. Theor. Biol. 295, 194–203 (2012)
H.L. Smith, H.R. Thieme, Dynamical Systems and Population Persistence, Graduate Studies in Mathematics, (American Mathematical Society, Providence, 2011)
P. Taylor, L. Jonker, Evolutionary stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)
H.R. Thieme, Uniform persistence and permanence for non-autonomous semiflows in population biology. Math. Biosci. 166, 173–201 (2000)
S. Xia, J. Liu, A computational approach to characterizing the impact of social influence on individuals’ vaccination decision making. PLoS ONE 8, e60373 (2013)
S. Xia, J. Liu, A belief-based model for characterizing the spread of awareness and its impacts on individuals’ vaccination decisions. J. R. Soc. B 11, 20140013 (2014)
S. Xia, J. Liu, W. Cheung, Identifying the relative priorities of subpopulations for containing infectious disease spread. PLoS ONE 8, e65271 (2013)
F. Xu, R. Cressman, Disease control through voluntary vaccination decisions based on the smoothed best response. Comput. Math. Methods Med. 2014, 14 (2014)
J. Yang, Y. Chen, Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate. J. Bio. Dyn., 12(1), 789–816
J. Yang, M. Martcheva, L. Wang, Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence. Math. Biosci. 268, 1–8 (2015)
J. Yang, M. Martcheva, Y. Chen, Imitation dynamics of vaccine decision-making behaviours based on the game theory. J. Biol. Dyn. 10, 31–58 (2016)
K. Yosida, Functional Analysis, 2nd edn. (Springer, Berlin/Heidelberg/New York, 1968)
H. Zhang, F. Fu, W. Zhang, B. Wang, Rational behavior is a “double-edged sword” when considering voluntary vaccination. Phys. A 391, 4807–4815 (2012)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Li, XZ., Yang, J., Martcheva, M. (2020). Age-Since-Infection Structured Models Based on Game Theory. In: Age Structured Epidemic Modeling. Interdisciplinary Applied Mathematics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-42496-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-42496-1_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-42495-4
Online ISBN: 978-3-030-42496-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)