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Liu Y, Wu B. Coevolution of vaccination behavior and perceived vaccination risk can lead to a stag-hunt-like game. Phys Rev E 2022; 106:034308. [PMID: 36266897 DOI: 10.1103/physreve.106.034308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2021] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
Voluntary vaccination is effective to prevent infectious diseases from spreading. Both vaccination behavior and cognition of the vaccination risk play important roles in individual vaccination decision making. However, it is not clear how the coevolution of the two shapes population-wide vaccination behavior. We establish a coupled dynamics of epidemic, vaccination behavior, and perceived vaccination risk with three different time scales. We assume that the increase of vaccination level inhibits the rise of perceived vaccination risk, and the increase of perceived vaccination risk inhibits the rise of vaccination level. It is shown that the resulting vaccination behavior is similar to the stag-hunt game, provided that the basic reproductive ratio is moderate and that the epidemic dynamics evolves sufficiently fast. This is in contrast with the previous view that vaccination is a snowdriftlike game. And we find that epidemic breaks out repeatedly and eventually leads to vaccine scares if these three dynamics evolve on a similar time scale. Furthermore, we propose some ways to promote vaccination behavior, such as controlling side-effect bias and perceived vaccination costs. Our work sheds light on epidemic control via vaccination by taking into account the coevolutionary dynamics of cognition and behavior.
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Affiliation(s)
- Yuan Liu
- School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Bin Wu
- School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
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2
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Ge J, Wang W. Vaccination games in prevention of infectious diseases with application to COVID-19. CHAOS, SOLITONS, AND FRACTALS 2022; 161:112294. [PMID: 35702367 PMCID: PMC9186443 DOI: 10.1016/j.chaos.2022.112294] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Revised: 05/30/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
Vaccination coverage is crucial for disease prevention and control. An appropriate combination of compulsory vaccination with voluntary vaccination is necessary to achieve the goal of herd immunity for some epidemic diseases such as measles and COVID-19. A mathematical model is proposed that incorporates both compulsory vaccination and voluntary vaccination, where a decision of voluntary vaccination is made on the basis of game evaluation by comparing the expected returns of different strategies. It is shown that the threshold of disease invasion is determined by the reproduction numbers, and an over-response in magnitude or information interval in the dynamic games could induce periodic oscillations from the Hopf bifurcation. The theoretical results are applied to COVID-19 to find out the strategies for protective immune barrier against virus variants.
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Affiliation(s)
- Jingwen Ge
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
| | - Wendi Wang
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
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Xia K. The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism. BMC Ecol Evol 2021; 21:152. [PMID: 34348658 PMCID: PMC8336419 DOI: 10.1186/s12862-021-01847-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 06/03/2021] [Indexed: 11/16/2022] Open
Abstract
BACKGROUND In recent years, the average abundance function has attracted much attention as it reflects the degree of cooperation in the population. Then it is significant to analyse how average abundance functions can be increased to promote the proliferation of cooperative behaviour. However, further theoretical analysis for average abundance function with mutation under redistribution mechanism is still lacking. Furthermore, the theoretical basis for the corresponding numerical simulation is not sufficiently understood. RESULTS We have deduced the approximate expressions of average abundance function with mutation under redistribution mechanism on the basis of different levels of selection intensity [Formula: see text] (sufficiently small and large enough). In addition, we have analysed the influence of the size of group d, multiplication factor r, cost c, aspiration level [Formula: see text] on average abundance function from both quantitative and qualitative aspects. CONCLUSIONS (1) The approximate expression will become the linear equation related to selection intensity when [Formula: see text] is sufficiently small. (2) On one hand, approximation expression when [Formula: see text] is large enough is not available when r is small and m is large. On the other hand, this approximation expression will become more reliable when [Formula: see text] is larger. (3) On the basis of the expected payoff function [Formula: see text] and function [Formula: see text], the corresponding results for the effects of parameters (d,r,c,[Formula: see text]) on average abundance function [Formula: see text] have been explained.
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Affiliation(s)
- Ke Xia
- School of Economics, Zhengzhou University of Aeronautics, Zhengzhou, China.
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Wang G, Su Q, Wang L. Evolution of state-dependent strategies in stochastic games. J Theor Biol 2021; 527:110818. [PMID: 34181968 DOI: 10.1016/j.jtbi.2021.110818] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 06/06/2021] [Accepted: 06/22/2021] [Indexed: 10/21/2022]
Abstract
In a population of interacting individuals, the environment for interactions often changes due to individuals' behaviors, which in turn drive the evolution of individuals' behaviors. The interplay between the environment and individuals' behaviors has been demonstrated to remarkably influence the evolutionary outcomes. In reality, in highly cognitive species such as social primates and human beings, individuals are often capable of perceiving the environment change and then differentiate their strategies across different environment states. We propose a model of environmental feedback with state-dependent strategies: individuals have perceptions of distinct environment states and therefore take distinct sub-strategies under each of them; based on the sub-strategy, individuals then decide their behaviors; their behaviors subsequently modify the environment state. We use the theory of stochastic games and evolutionary dynamics to analyze this idea. We find that when environment changes slower than behaviors, state-dependent strategies (i.e. taking different sub-strategies under different environment states) can outperform state-independent strategies (i.e. taking an identical sub-strategy under all environment states), such as Win-Stay, Lose-Shift, the most leading strategy among state-independent strategies. The intuition is that delayed environmental feedback provides chances for individuals with state-dependent strategies to exploit those with state-independent strategies. Our results hold (1) in both well-mixed and structured populations; (2) when the environment switches between two or more states. Furthermore, the environment changing rate decides if state-dependent strategies benefit global cooperation. The evolution sees the rise of the cooperation level for fast environment switching and the decrease otherwise. Our work stresses that individuals' perceptions of different environment states are beneficial to their survival and social prosperity in a changing world.
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Affiliation(s)
- Guocheng Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China
| | - Qi Su
- Center for Mathematical Biology, University of Pennsylvania, Philadelphia, PA 19104, USA; Department of Mathematics, University of Pennsylvania, Philadelphia, PA19104, USA; Department of Biology, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China; Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing 100871, China.
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Chang SL, Piraveenan M, Pattison P, Prokopenko M. Game theoretic modelling of infectious disease dynamics and intervention methods: a review. JOURNAL OF BIOLOGICAL DYNAMICS 2020; 14:57-89. [PMID: 31996099 DOI: 10.1080/17513758.2020.1720322] [Citation(s) in RCA: 58] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
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).
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Affiliation(s)
- Sheryl L Chang
- Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia
| | - Mahendra Piraveenan
- Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia
- Charles Perkins Centre, The University of Sydney, John Hopkins Drive, Sydney, Australia
| | - Philippa Pattison
- Office of the Deputy Vice-Chancellor (Education), The University of Sydney, Sydney, Australia
| | - Mikhail Prokopenko
- Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia
- Marie Bashir Institute for Infectious Diseases and Biosecurity, The University of Sydney, Sydney, Australia
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Liu MX, Zhang RP, Xie BL. The impact of behavioral change on the epidemic under the benefit comparison. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2020; 17:3412-3425. [PMID: 32987536 DOI: 10.3934/mbe.2020193] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Human behavior has a major impact on the spread of the disease during an epidemic. At the same time, the spread of disease has an impact on human behavior. In this paper, we propose a coupled model of human behavior and disease transmission, take into account both individual-based risk assessment and neighbor-based replicator dynamics. The transmission threshold of epidemic disease and the stability of disease-free equilibrium point are analyzed. Some numerical simulations are carried out for the system. Three kinds of return matrices are considered and analyzed one by one. The simulation results show that the change of human behavior can effectively inhibit the spread of the disease, individual-based risk assessments had a stronger effect on disease suppression, but also more hitchhikers. This work contributes to the study of the relationship between human behavior and disease epidemics.
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Affiliation(s)
- Mao Xing Liu
- School of Science, North University of China, Taiyuan 030051, China
| | - Rong Ping Zhang
- School of Science, North University of China, Taiyuan 030051, China
| | - Bo Li Xie
- School of Science, North University of China, Taiyuan 030051, China
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Wei Y, Lin Y, Wu B. Vaccination dilemma on an evolving social network. J Theor Biol 2019; 483:109978. [DOI: 10.1016/j.jtbi.2019.08.009] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Revised: 08/02/2019] [Accepted: 08/08/2019] [Indexed: 12/15/2022]
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Chang SL, Piraveenan M, Prokopenko M. The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2019; 16:E2477. [PMID: 31336761 PMCID: PMC6678199 DOI: 10.3390/ijerph16142477] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Revised: 07/08/2019] [Accepted: 07/09/2019] [Indexed: 01/08/2023]
Abstract
We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the resultant vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions for the basic reproduction number R 0 for the proposed SIR-network models. Furthermore, we simulate the epidemic dynamics over time for the considered models, and show that if individuals are sufficiently responsive towards the changes in the disease prevalence, then the more expansive travelling patterns encourage convergence to the endemic, mixed equilibria. On the contrary, if individuals are insensitive to changes in the disease prevalence, we find that they tend to remain unvaccinated. Our results concur with earlier studies in showing that residents from highly connected residential areas are more likely to get vaccinated. We also show that the existence of the individuals committed to receiving vaccination reduces R 0 and delays the disease prevalence, and thus is essential to containing epidemics.
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Affiliation(s)
- Sheryl Le Chang
- Complex Systems Research Group, Faculty of Engineering, The University of Sydney, Sydney, NSW 2006, Australia.
| | - Mahendra Piraveenan
- Complex Systems Research Group, Faculty of Engineering, The University of Sydney, Sydney, NSW 2006, Australia
- Charles Perkins Centre, The University of Sydney, John Hopkins Drive, Camperdown, NSW 2006, Australia
| | - Mikhail Prokopenko
- Complex Systems Research Group, Faculty of Engineering, The University of Sydney, Sydney, NSW 2006, Australia
- Marie Bashir Institute for Infectious Diseases and Biosecurity, The University of Sydney, Westmead, NSW 2145, Australia
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