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Game theoretic modelling of infectious disease dynamics and intervention methods: a review. (English) Zbl 1447.92405

Summary: We review research studies which use game theory to model the decision-making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. The literature is classified based on (i) type of population modelling (classical or network-based), (ii) frequency of the game (non-repeated or repeated), and (iii) type of strategy adoption (self-learning or imitation). The choice of model is shown to depend on many factors such as the immunity to the disease, the strength of immunity conferred by the vaccine, the size of population and the level of mixing therein. We highlight that while early studies used classical compartmental modelling with self-learning games, in recent years, there is a substantial growth of network-based modelling with imitation games. The review indicates that game theory continues to be an effective tool to model decision-making by individuals with respect to intervention (vaccination or social distancing).

MSC:

92D30 Epidemiology
92C60 Medical epidemiology
91A80 Applications of game theory
91A35 Decision theory for games
91A20 Multistage and repeated games
92-02 Research exposition (monographs, survey articles) pertaining to biology

References:

[1] A. Adiga, S. Venkat, A. Vullikanti, To delay or not: temporal vaccination games on networks, IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications, San Francisco, CA, USA, 2016. [Google Scholar]
[2] L.J.S. Allen, An introduction to stochastic epidemic models, Chap. 3, in Mathematical Epidemiology, Springer-Verlag, Berlin, 2008. [Google Scholar] · Zbl 1206.92022
[3] R.M. Anderson and R.M. May, Infectious Diseases of Humans, Oxford University Press, Oxford, 1992. [Google Scholar]
[4] A. Barabàsi, The scale-free property, Chap. 4, in Network Science, Cambridge University Press, Cambridge, UK, 2016. [Google Scholar] · Zbl 1353.94001
[5] S. Basu, G.B. Chapman, and A.P. Galvani, Integrating epidemiology, psychology, and economic to achieve HPV vaccination target, Proc. Natl. Acad. Sci. 105 (2008), pp. 19018-19023. doi: 10.1073/pnas.0808114105[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[6] C.T. Bauch, Imitation dynamics predict vaccinating behaviour, Proc. R. Soc. B 272 (2005), pp. 1669-1675. doi: 10.1098/rspb.2005.3153[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[7] C.T. Bauch and S. Bhattacharyya, Evolutionary game theory and social learning can determine how vaccine scares unfold, PLoS Comput. Biol. 8 (2012), p. e1002452. doi: 10.1371/journal.pcbi.1002452[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[8] C. Bauch and D.J.D. Earn, Vaccination and the theory of games, Proc. Natl. Acad. Sci. 101 (2004), pp. 13391-13394. doi: 10.1073/pnas.0403823101[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1064.91029
[9] C. Bauch, A.P. Galvani, and D. Earn, Group interest versus self-interest in smallpox vaccination policy, Proc. Natl. Acad. Sci. 100 (2003), pp. 10564-10567. doi: 10.1073/pnas.1731324100[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1065.92038
[10] S. Bhattacharyya and C.T. Bauch, A game dynamic model for delayer strategies in vaccinating behaviour for paediatric infectious diseases, J. Theor. Biol. 267 (2010), pp. 276-282. doi: 10.1016/j.jtbi.2010.09.005[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1410.92058
[11] S. Bhattacharyya and C.T. Bauch, “Wait and see” vaccinating behaviour during a pandemic: a game theoretic analysis, Vaccine 29 (2011), pp. 5519-5525. doi: 10.1016/j.vaccine.2011.05.028[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[12] S. Bhattacharyya, A. Vutha, A. Lloyd, and C. Bauch, The impact of rare but severe vaccine adverse events on behaviour-disease dynamics: a network model, Sci. Rep. 9 (2019), pp. 1-13. doi: 10.1038/s41598-018-37186-2[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[13] F. Brauer, Compartmental models in epidemiology, in Chap. 2, Mathematical Epidemiology, Springer-Verlag, Berlin, 2008. [Google Scholar] · Zbl 1206.92023
[14] R. Breban, Health newscasts for increasing influenza vaccination coverages: an inductive reasoning game approach, PLoS One 6 (2011), pp. 1-10. doi: 10.1371/journal.pone.0028300[Crossref], [Web of Science ®], [Google Scholar]
[15] R. Breban, R. Vardavas, and S. Blower, Inductive reasoning games as influenza vaccination models: mean field analysis, Phys. Rev. E 76 (2007), p. 031127. doi: 10.1103/PhysRevE.76.031127[Crossref], [Web of Science ®], [Google Scholar]
[16] F. Chen, Rational behavioral response and the transmission of STDs, Theor. Popul Biol. 66 (2004), pp. 307-316. doi: 10.1016/j.tpb.2004.07.004[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1073.92042
[17] O.M. Cliff, N. Harding, M. Piraveenan, Y. Erten, M. Gambhir, and M. Prokopenko, Investigating spatiotemporal dynamics and synchrony of influenza epidemics in Australia: an agent-based modelling approach, Simul. Modell. Pract. Theory 87 (2018), pp. 412-431. doi: 10.1016/j.simpat.2018.07.005[Crossref], [Web of Science ®], [Google Scholar]
[18] O.M. Cliff, V. Sintchenko, T.C. Sorrell, K. Vadlamudi, N. McLean, and M. Prokopenko, Network properties of salmonella epidemics, Sci. Rep. 9 (2019), pp. 1-6. doi: 10.1038/s41598-019-42582-3[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[19] D.M. Cornforth, T. Reluga, E. Shim, C.T. Bauch, A.P. Galvani, and L.A. Meyers, Erratic flu vaccination emerges from short-sighted behavior in contact networks, PLoS Comput. Biol. 7 (2011), pp. 1-11. doi: 10.1371/journal.pcbi.1001062[Crossref], [Web of Science ®], [Google Scholar]
[20] A. d’Onofrio, P. Manfredi, and P. Poletti, The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach, J. Theor. Biol. 273 (2011), pp. 63-71. doi: 10.1016/j.jtbi.2010.12.029[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1405.92149
[21] A. d’Onofrio, P. Manfredi, and E. Salinelli, Vaccinating behaviour, information, and the dynamics of sir vaccine preventable diseases, Theor. Popul Biol. 71 (2007), pp. 301-317. doi: 10.1016/j.tpb.2007.01.001[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1124.92029
[22] S. Dorogovtsev and J. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW, Oxford University Press, Oxford, 2003. [Crossref], [Google Scholar] · Zbl 1109.68537
[23] C. Eksin, J. Shamma, and J. Weitz, Disease dynamics in a stochastic network game: a little empathy goes a long way in averting outbreaks, Sci. Rep. 14 (2017), p. 44122. doi: 10.1038/srep44122[Crossref], [Google Scholar]
[24] E. Erten, J. Lizier, M. Piraveenan, and M. Prokopenko, Criticality and information dynamics in epidemiological models, Entropy 19 (2017), p. 194. doi: 10.3390/e19050194[Crossref], [Web of Science ®], [Google Scholar]
[25] S. Eubank, H. Guclu, V.A. Kumar, M.V. Marathe, A. Srinivasan, Z. Toroczkai, and N. Wang, Modelling disease outbreaks in realistic urban social networks, Nature 429 (2004), p. 180. doi: 10.1038/nature02541[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[26] X. Feng, W. Bin, and W. Long, Voluntary vaccination dilemma with evolving psychological perceptions, J. Theor. Biol. 439 (2018), pp. 65-75. doi: 10.1016/j.jtbi.2017.11.011[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1397.92631
[27] P. Fine and J. Clarkson, Measles in England and Wales-I: an analysis of factors underlying seasonal patterns, Int. J. Epidemiol. 11 (1982), pp. 5-14. doi: 10.1093/ije/11.1.5[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[28] P. Fine and J. Clarkson, Individual versus public priorities in the determination of optimal vaccination policies, Am. J. Epidemiol. 124 (1986), pp. 1012-1020. doi: 10.1093/oxfordjournals.aje.a114471[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[29] F. Fu, D. Rosenbloom, L. Wang, and M. Nowak, Imitation dynamics of vaccination behaviour on social networks, Proc. R. Soc. B 278 (2010), pp. 42-49. doi: 10.1098/rspb.2010.1107[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[30] E. Fukuda, Chap. 6 Pandemic Analysis and Evolutionary Games, in, Fundamentals of evolutionary game theory and its applications, Springer, Japan, 2015, pp. 183-209. [Google Scholar] · Zbl 1326.91001
[31] S. Funk, M. Salathé, and V.A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: a review, J. R. Soc. Interface 7 (2010), pp. 1247-1256. doi: 10.1098/rsif.2010.0142[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[32] A. Galvani, T. Reluga, and G. Chapman, Long-standing influenza vaccination policy is in accord with individual self-interest but not with the utilitarian optimum, Proc. Natl. Acad. Sci. 104 (2007), pp. 5692-5697. doi: 10.1073/pnas.0606774104[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[33] T.C. Germann, K. Kadau, I.M. Longini, and C.A. Macken, Mitigation strategies for pandemic influenza in the United States, Proc. Natl. Acad. Sci. 103 (2006), pp. 5935-5940. doi: 10.1073/pnas.0601266103[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[34] D. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81 (1977), pp. 2340-2361. doi: 10.1021/j100540a008[Crossref], [Web of Science ®], [Google Scholar]
[35] J. Goeree, C. Holt, and T. Palfrey, Quantal Response Equilibrium: A Stochastic Theory of Games, Princeton University Press, Princeton, 2016. [Crossref], [Google Scholar] · Zbl 1390.91003
[36] N. Harding, R. Nigmatullin, and M. Prokopenko, Thermodynamic efficiency of contagions: a statistical mechanical analysis of the sis epidemic model, Interface Focus 8 (2018), p. 20180036. doi: 10.1098/rsfs.2018.0036[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[37] D. Kasthurirathna and M. Piraveenan, Emergence of scale-free characteristics in socio-ecological systems with bounded rationality, Nat. Sci. Rep. 5 (2015), p. 10448. doi: 10.1038/srep10448[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[38] D. Kasthurirathna, M. Piraveenan, and S. Uddin, Modeling networked systems using the topologically distributed bounded rationality framework, Complexity 21 (2016), pp. 123-137. doi: 10.1002/cplx.21789[Crossref], [Web of Science ®], [Google Scholar]
[39] M. Keeling and K.T.D. Eames, Networks and epidemic models, J. R. Soc. Interface 2 (2005), pp. 295-307. doi: 10.1098/rsif.2005.0051[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[40] H. Klarman, J. Francis, and G. Rosenthal, Cost-effectiveness analysis applied to the treatment of chronic renal disease, Med. Care 6 (1968), pp. 48-54. doi: 10.1097/00005650-196801000-00005[Crossref], [Web of Science ®], [Google Scholar]
[41] Q. Li, M. Li, L. Lv, C. Guo, and K. Lu, A new prediction model of infectious diseases with vaccination strategies based on evolutionary game theory, Chaos Solit. Fractals 104 (2017), pp. 51-60. doi: 10.1016/j.chaos.2017.07.022[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1380.92074
[42] A. Liberati, D.G. Altman, J. Tetzlaff, C. Mulrow, P.C. Gøtzsche, J.P.A. Ioannidis, M. Clarke, P.J.Devereaux, J. Kleijnen, and D. Moher, The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate health care interventions: explanation and elaboration, PLoS Med. 6 (2009), p. e1000100. doi: 10.1371/journal.pmed.1000100[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[43] J. Liu, B.F. Kochin, Y.I. Tekle, and A.P. Galvani, Epidemiological game-theory dynamics of chickenpox vaccination in the USA and Israel, J. R. Soc. Interface 9 (2012), pp. 68-76. doi: 10.1098/rsif.2011.0001[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[44] X. Liu, Z. Wu, and L. Zhang, Impact of committed individuals on vaccination behaviour, Phys. Rev. E 86 (2012), p. 051132. [Crossref], [Web of Science ®], [Google Scholar]
[45] I.M. Longini, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakul, D.A. Cummings, and M.E. Halloran, Containing pandemic influenza at the source, Science 309 (2005), pp. 1083-1087. doi: 10.1126/science.1115717[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[46] J. Nash, Equilibrium points in n-person game, Proc. Natl. Acad. Sci. 36 (1949), pp. 48-49. doi: 10.1073/pnas.36.1.48[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0036.01104
[47] M. Ndeffo Mbah, J. Liu, C. Bauch, Y. Tekel, J. Medlock, L. Meyers, and A. Galvani, The impact of imitation on vaccination behavior in social contact networks, PLoS Comput. Biol. 8 (2012), p. e1002469. doi: 10.1371/journal.pcbi.1002469[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[48] C. Nowzari, V.M. Preciado, and G.J. Pappas, Analysis and control of epidemics: A survey of spreading processes on complex networks, IEEE Control Syst. Mag. 36 (2016), pp. 26-46. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1476.92046
[49] R. Pastor-Satorras, C. Castellano, P. Mieghem, and A. Vespignani, Epidemic processes in complex networks, Rev. Mod. Phys. 87 (2015), pp. 926-973. doi: 10.1103/RevModPhys.87.925[Crossref], [Web of Science ®], [Google Scholar]
[50] P. Pattison and G. Robins, Neighbourhood-based models for social networks, Sociol. Method. 32 (2002), pp. 301-337. doi: 10.1111/1467-9531.00119[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1127.91380
[51] P.E. Pattison, G. Robins, Modelling the structure and dynamics of network-based social systems, 19th International Congress on Modelling and Simulation, Perth, Western Australia, 2011. [Google Scholar]
[52] A. Perisic and C. Bauch, A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks, BMC Infect. Dis. 9 (2009), p. 77. doi: 10.1186/1471-2334-9-77[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[53] A. Perisic and C. Bauch, Social contact networks and disease eradicability under voluntary vaccination, PLoS One 5 (2009), p. e1000280. [Google Scholar]
[54] M. Piraveenan, M. Prokopenko, and L. Hossain, Percolation centrality: quantifying graph-theoretic impact of nodes during percolation in networks, PLoS One 8 (2013), p. e53095. doi: 10.1371/journal.pone.0053095[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[55] P. Poletti, M. Ajelli, and S. Merler, The effect of risk perception on the 2009 H1N1 pandemic influenza dynamics, PLoS One 6 (2011), pp. 1-7. [Crossref], [Google Scholar]
[56] P. Poletti, M. Ajelli, and S. Merler, Risk perception and effectiveness of uncoordinated behavioural responses in an emerging epidemic, Math. Biosci. 238 (2012), pp. 80-89. doi: 10.1016/j.mbs.2012.04.003[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1316.92089
[57] P. Poletti, B. Caprile, M. Ajelli, A. Pugliese, and S. Merler, Spontaneous behavioural changes in response to epidemics, J. Theor. Biol. 260 (2009), pp. 31-40. doi: 10.1016/j.jtbi.2009.04.029[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1402.92404
[58] T.C. Reluga, C.T. Bauch, and A.P. Galvani, Evolving public perceptions and stability in vaccine uptake, Math. Biosci. 204 (2006), pp. 185-198. doi: 10.1016/j.mbs.2006.08.015[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1104.92042
[59] T. Reluga, An SIS epidemiology game with two subpopulations, J. Biol. Dyn. 3 (2009), pp. 515-531. doi: 10.1080/17513750802638399[Taylor & Francis Online], [Google Scholar] · Zbl 1342.92277
[60] T. Reluga, Game theory of social distancing in response to an epidemic, PLoS Comput. Biol. 6 (2010), pp. 1-9. doi: 10.1371/journal.pcbi.1000793[Crossref], [Web of Science ®], [Google Scholar]
[61] T. Reluga and A.P. Galvani, A general approach for population games with application to vaccination, Math. Biosci. 230 (2011), pp. 67-78. doi: 10.1016/j.mbs.2011.01.003[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1211.92049
[62] T. Reluga and J. Li, Games of age-dependent prevention of chronic infections by social distancing, Math. Biol. 66 (2013), pp. 1527-1553. doi: 10.1007/s00285-012-0543-8[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1267.91013
[63] S. Saha, A. Adiga, B.A. Prakash, Approximation algorithms for reducing the spectral radius to control epidemic spread, Proceedings of the 2015 SIAM International Conference on Data Mining, Vancouver, British Columbia, Canada, 2015, pp. 568-576. [Google Scholar]
[64] E. Shim, L.A. Meyers, and A.P. Galvani, Optimal H1N1 vaccination strategies based on self-interest versus group interest, BMC Public Health 11 (2011), p. S4. doi: 10.1186/1471-2458-11-S1-S4[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[65] E. Shim, B. Kochin, and A. Galvani, Insights from epidemiological game theory into gender-specific vaccination against rubella, Math. Biosci. Eng. 6(4) (2009), pp. 839-854. doi: 10.3934/mbe.2009.6.839[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1178.92041
[66] E. Shim, G.B. Chapman, J.P. Townsend, and G.P. Galvani, The influence of altruism on influenza vaccination decisions, J. R. Soc. Interface 9 (2012), pp. 2234-2243. doi: 10.1098/rsif.2012.0115[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[67] L. Thomas, Games, Theory and Applications, Dover Publication, Inc., Mineola, NY, 2003. [Google Scholar] · Zbl 1140.91023
[68] D. Thorrinton, M. Ramsay, A.J. van Hoek, W.J. Edmunds, R. Vivancos, A. Bukasa, and K. Eames, The effect of measles on health-related quality of life: a patient-based survey, PLoS One 9 (2014), pp. 1-9. [Google Scholar]
[69] R. Vardavas, R. Breban, and S. Blower, Can influenza epidemics be prevented by voluntary vaccination? PLoS Comput. Biol. 3 (2007), pp. 796-802. doi: 10.1371/journal.pcbi.0030085[Crossref], [Web of Science ®], [Google Scholar]
[70] Z. Wang, M.A. Andrews, Z. Wu, L. Wang, and C.T. Bauch, Coupled disease-behavior dynamics on complex networks: A review, Phys. Life Rev. 15 (2015), pp. 1-29. doi: 10.1016/j.plrev.2015.07.006[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[71] D. Watts and S. Strogatz, Collective dynamics of small-world networks, Nature 393 (1998), pp. 440-442. doi: 10.1038/30918[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1368.05139
[72] J. Webbs, Game Theory: Decisions, Interaction and Evolution, Springer, London, 2007. [Google Scholar] · Zbl 1107.91001
[73] C.R. Wells, J. Tchuenche, L. Meyers, A. Galvani, and C. Bauch, Impact of imitation processes on the effectiveness of ring vaccination, Bull. Math. Biol. 73 (2011), pp. 2748-2772. doi: 10.1007/s11538-011-9646-4[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1334.92435
[74] R. Bonita, R. Beaglehole, T. Kjellstrom, WHO, Basic Epidemiology. 2nd Edition,WHO Press, Geneva, Switzerland, 2006. [Google Scholar]
[75] C. Zachreson, K.M. Fair, O.M. Cliff, N. Harding, M. Piraveenan, and M. Prokopenko, Urbanization affects peak timing, prevalence, and bimodality of influenza pandemics in Australia: results of a census-calibrated model, Sci. Adv. 4 (2018), p. eaau5294. doi: 10.1126/sciadv.aau5294[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[76] H. Zhang, F. Fu, W. Zhang, and B. Wang, Rational behaviour is a ‘double-edged sword’ when considering voluntary vaccination, Phys. A 391 (2012), pp. 4807-4815. doi: 10.1016/j.physa.2012.05.009[Crossref], [Web of Science ®], [Google Scholar]
[77] H. Zhang, J. Zhang, C. Zhou, M. Small, and B. Wang, Hub nodes inhibit the outbreak of epidemic under voluntary vaccination, New J. Phys. 12 (2010), p. 023015. [Crossref], [Web of Science ®], [Google Scholar]
[78] Y. Zhang, The impact of other-regarding tendencies on the spatial vaccination network, Chaos Solit. Fractals 2013 (2013), pp. 209-215. doi: 10.1016/j.chaos.2013.08.014[Crossref], [Google Scholar] · Zbl 1349.92156
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