The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model
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
Marie Bashir Institute for Infectious Diseases and Biosecurity, The University of Sydney, Westmead, NSW 2145, Australia
Author to whom correspondence should be addressed.
Received: 7 May 2019 / Revised: 8 July 2019 / Accepted: 9 July 2019 / Published: 11 July 2019
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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
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
and delays the disease prevalence, and thus is essential to containing epidemics.
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Chang, S.L.; Piraveenan, M.; Prokopenko, M. The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model. Int. J. Environ. Res. Public Health 2019, 16, 2477.
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(14):2477.
Chang, Sheryl L.; Piraveenan, Mahendra; Prokopenko, Mikhail. 2019. "The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model." Int. J. Environ. Res. Public Health 16, no. 14: 2477.
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