The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model

• Main Authors: Sheryl Le Chang, Mahendra Piraveenan, Mikhail Prokopenko
• Format: Article
• Language: English
• Published: MDPI AG 2019-07-01
• Series: International Journal of Environmental Research and Public Health
• Subjects: vaccination; epidemic modelling; SIR model; strategy imitation; herd immunity; Erdös-Rényi random networks; greater Sydney commuting network
• Online Access: https://www.mdpi.com/1660-4601/16/14/2477

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 <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> and delays the disease prevalence, and thus is essential to containing epidemics.