The impact of behavioral change on the epidemic under the benefit comparison

Maoxing Liu; Rongping Zhang; Boli Xie; Maoxing Liu; Rongping Zhang; Boli Xie

doi:10.3934/mbe.2020193

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3412-3425. doi: 10.3934/mbe.2020193

Previous Article Next Article

Research article Special Issues

The impact of behavioral change on the epidemic under the benefit comparison

School of Science, North University of China, Taiyuan 030051, China

Received: 07 April 2020 Accepted: 20 April 2020 Published: 30 April 2020

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.
- behavioral change,
- epidemic spread,
- game theory,
- stability,
- hitchhiking
Citation: Maoxing Liu, Rongping Zhang, Boli Xie. The impact of behavioral change on the epidemic under the benefit comparison[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3412-3425. doi: 10.3934/mbe.2020193

Related Papers:

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.

References

[1]	F. Verelst, L. Willem, P. Beutels, Behavioural change models for infectious disease transmission: A systematic review (2010-2015), J. R. Soc. Interface, 13 (2016), 20160820. doi: 10.1098/rsif.2016.0820
[2]	J. T. F. Lau, X. L. Yang, H. Y. Tsui, E. Pang, SARS related preventive and risk behaviours practised by Hong Kong-mainland China cross border travellers during the outbreak of the SARS epidemic in Hong Kong, J. Epidemiol. Community Health, 58 (2004), 988-996. doi: 10.1136/jech.2003.017483
[3]	J. T. Vietri, M. Li, A. P. Galvani, G. B. Chapman, Vaccinating to help ourselves and others, Med. Decis. Making, 32 (2012), 447-458. doi: 10.1177/0272989X11427762
[4]	S. Abdelmalek, S. Bendoukha, Global asymptotic stability of a diffusive SVIR epidemic model with immigration of individuals, Electron. J. Differ. Equations, 284 (2016), 1-14.
[5]	C. R. Cai, Z. X. Wu, J. Y. Guan, Behavior of susceptible-vaccinated-infected-recovered epidemics with diversity in the infection rate of individuals, Phys. Rev. E, 88 (2013), 062805. doi: 10.1103/PhysRevE.88.062805
[6]	C. Deng, H. J. Gao, Stability of SVIR system with random perturbations, Inter. J. Biomath., 5 (2012).
[7]	T. C. Reluga, C. T. Bergstrom, Game theory of social distancing in response to an epidemic, PLoS Comput. Biol., 6 (2010).
[8]	E. P. Fenichel, C. Castillo-Chavez, M. G. Ceddia, G. Chowell, P. A. G. Parra, G. J. Hickling, et al., Adaptive human behavior in epidemiological models, Proc. Natl. Acad. Sci., 108 (2011), 6306-6311.
[9]	E. P. Fenichel, X. X. Wang, The mchanism and phenomena of adaptive human behavior during an epidemic and the role of information, in Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases, Springer, (2013), 153-168.
[10]	P. C. Zhu, Q. Zhi, Y. M. Guo, Z. Wang, Analysis of epidemic spreading process in adaptive networks, IEEE Trans. Circuits Syst. II: Express Briefs, 66 (2018), 1252-1256.
[11]	Y. Z. Zhou, Y. J. Xia, Epidemic spreading on weighted adaptive networks, Phys. A, 399 (2014), 16-23. doi: 10.1016/j.physa.2013.12.036
[12]	T. Li, X. D. Liu, J. Wu, C. Wan, Z. H. Guan, Y. M. Wang, An epidemic spreading model on adaptive scale-free networks with feedback mechanism, Physica A, 450 (2016), 649-656. doi: 10.1016/j.physa.2016.01.045
[13]	S. L. Chang, M. Piraveenan, P. Pattison, M. Prokopenko, Game theoretic modelling of infectious disease dynamics and intervention methods: A review, J. Biol. Dyn., 14 (2019), 57-89.
[14]	H. Zhang, F. Fu, W. Zhang, B. Wang, Rational behavior is a double-edged sword when considering voluntary vaccination, Phys. A, 391 (2012), 4807-4815. doi: 10.1016/j.physa.2012.05.009
[15]	Y. Zhang, The impact of other-regarding tendencies on the spatial vaccination game, Chaos Solitons Fractals, 56 (2013), 209-215. doi: 10.1016/j.chaos.2013.08.014
[16]	Q. Li, M. C. Li, L. Lv, C. Guo, K. Lu, A new prediction model of infectious diseases with vaccination strategies based on evolutionary game theory, Chaos Solitons Fractals, 104 (2017), 51-60. doi: 10.1016/j.chaos.2017.07.022
[17]	K. Kuga, J. Tanimoto, Which is more effective for suppressing an infectious disease: Imperfect vaccination or defense against contagion?, J. Stat. Mech. Theory Exp., 2018 (2018), 023407. doi: 10.1088/1742-5468/aaac3c
[18]	K. M. A. Kabir, K. Kuga, J. Tanimoto, Effect of information spreading to suppress the disease contagion on the epidemic vaccination game, Chaos Solitons Fractals, 119 (2019), 180-187. doi: 10.1016/j.chaos.2018.12.023
[19]	C. T. Bauch, D. J. D. Earn, Vaccination and the theory of games, Proc. Natl. Acad. Sci., 101 (2004), 13391-13394. doi: 10.1073/pnas.0403823101
[20]	T. Dominic, R. Mary, V. H. A. Jan, W. J. Edmunds, R. Vivancos, A. Bukasa, et al., The effect of measles on health-related quality of life: A patient-based survey, PLoS ONE, 9 (2014).
[21]	X. Feng, B. Wu, L. Wang, Voluntary vaccination dilemma with evolving psychological perceptions, J. Theor. Biol., 439 (2018), 65-75. doi: 10.1016/j.jtbi.2017.11.011
[22]	K. M. A. Kabir, J. Tanimoto, Evolutionary vaccination game approach in metapopulation migration model with information spreading on different graphs, Chaos Solitons Fractals, 120 (2019), 41-55. doi: 10.1016/j.chaos.2019.01.013
[23]	K. M. A. Kabir, M. Jusup, J. Tanimoto, Behavioral incentives in a vaccination-dilemma setting with optional treatment, Phys. Rev. E, 100 (2019), 062402. doi: 10.1103/PhysRevE.100.062402
[24]	K. Kuga, J. Tanimoto, M. Jusup, To vaccinate or not to vaccinate: A comprehensive study of vaccination-subsidizing policies with multi-agent simulations and mean-field modeling, J. Theor. Biol., 469 (2019), 107-126. doi: 10.1016/j.jtbi.2019.02.013
[25]	M. R. Arefin, K. M. A. Kabir1, J. Tanimoto. A mean-field vaccination game scheme to analyze the effect of a single vaccination strategy on a two-strain epidemic spreading, J. Stat. Mech. Theory Exp., 2020 (2020), 033501. doi: 10.1088/1742-5468/ab74c6
[26]	P. Poletti, B. Caprile, M. Ajelli, A. Pugliese, S. Merlera, Spontaneous behavioural changes in response to epidemics, J. Theor. Biol., 260 (2009), 31-40. doi: 10.1016/j.jtbi.2009.04.029
[27]	P. S. Romualdo, V. Alessandro, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200-3203. doi: 10.1103/PhysRevLett.86.3200
[28]	A. B. M. Nasiruzzaman, M. N. Akter, M. A. Mahmud, H. R. Pota, Exploration of power flow distribution to reveal scale-free characteristics in power grids, 2017 IEEE Power & Energy Society General Meeting, 2017. Available from: https://ieeexplore.ieee.org/abstract/document/8273917.
[29]	A. L. Barabasi, R. Albert, H. Jeong, Scale-free characteristics of random networks: the topology of the world-wide web, Physica A, 281 (2000), 69-77. doi: 10.1016/S0378-4371(00)00018-2
[30]	K. Dharshana, P. Mahendra, Emergence of scale-free characteristics in socio-ecological systems with bounded rationality, Sci. Rep., 5 (2015), 10448. doi: 10.1038/srep10448
[31]	P. Yang, Z. P. Xu, J. Feng, X. Fu, Feedback pinning control of collective behaviors aroused by epidemic spread on complex networks, Chaos, 29 (2019).
[32]	K. Li, Z. Ma, Z. Jia, M. Small, X Fu, Interplay between collective behavior and spreading dynamics on complex networks, Chaos, 29 (2012), 043113

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)