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. 2014 Feb 12;281(1780):20133172.
doi: 10.1098/rspb.2013.3172. Print 2014 Apr 7.

The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases

Affiliations

Affiliation

  • 1 Department of Mathematics and Statistics, University of Guelph, , Guelph, Ontario, Canada, Department of Applied Mathematics, University of Waterloo, , Waterloo, Ontario, Canada.

The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases

Tamer Oraby et al. Proc Biol Sci. .
. 2014 Feb 12;281(1780):20133172.
doi: 10.1098/rspb.2013.3172. Print 2014 Apr 7.

Affiliation

  • 1 Department of Mathematics and Statistics, University of Guelph, , Guelph, Ontario, Canada, Department of Applied Mathematics, University of Waterloo, , Waterloo, Ontario, Canada.

Erratum in

Abstract

Mathematical models that couple disease dynamics and vaccinating behaviour often assume that the incentive to vaccinate disappears if disease prevalence is zero. Hence, they predict that vaccine refusal should be the rule, and elimination should be difficult or impossible. In reality, countries with non-mandatory vaccination policies have usually been able to maintain elimination or very low incidence of paediatric infectious diseases for long periods of time. Here, we show that including injunctive social norms can reconcile such behaviour-incidence models to observations. Adding social norms to a coupled behaviour-incidence model enables the model to better explain pertussis vaccine uptake and disease dynamics in the UK from 1967 to 2010, in both the vaccine-scare years and the years of high vaccine coverage. The model also illustrates how a vaccine scare can perpetuate suboptimal vaccine coverage long after perceived risk has returned to baseline, pre-vaccine-scare levels. However, at other model parameter values, social norms can perpetuate depressed vaccine coverage during a vaccine scare well beyond the time when the population's baseline vaccine risk perception returns to pre-scare levels. Social norms can strongly suppress vaccine uptake despite frequent outbreaks, as observed in some small communities. Significant portions of the parameter space also exhibit bistability, meaning long-term outcomes depend on the initial conditions. Depending on the context, social norms can either support or hinder immunization goals.

Keywords: behaviour-incidence model; decision-making; paediatric immunization; peer pressure; social norms.

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Figures

Figure 1.

Figure 1.

Empirical and modelled ( a

Figure 1.

Empirical and modelled ( a , c , e ) pertussis vaccine coverage…

Figure 1.
Empirical and modelled (a,c,e) pertussis vaccine coverage and (b,d,f) pertussis incidence in the UK, (a,b) from 1971 to 1988 without injunctive social norms, (c,d) from 1967 to 2010 without injunctive social norms and (e,f) from 1967 to 2010 with injunctive social norms. The solid line is the empirical data and the dashed line is the best-fitting model.
Figure 2.

Figure 2.

The δ m parameter…

Figure 2.

The δ m parameter plane for the stability of model equilibria [Image:…

Figure 2.
The δm parameter plane for the stability of model equilibria [Image: see text], [Image: see text] and [Image: see text]. [Image: see text] (full vaccine coverage, disease-free) is stable in the hatched region below the thick black diagonal line. [Image: see text] (no vaccine coverage, endemic) is stable in the light grey region. [Image: see text] (partial vaccine coverage, endemic) is stable in the dark grey region on the left. Parameter values come from estimates in §3a. Estimated δ and m values are represented in the plane by the black dot. Other parameter values are σ = 1, κ = 1.69 yr1, β = 280 yr1, μ = 1/50 yr1 and γ = 365/22 yr1.
Figure 3.

Figure 3.

Simulations of ( a ,

Figure 3.

Simulations of ( a , c ) vaccine coverage and ( b ,

Figure 3.
Simulations of (a,c) vaccine coverage and (b,d) disease incidence for parameter values in the bistability regions of figure 2, converging either to [Image: see text] (dashed lines), [Image: see text] (solid lines in (c,d)) or stable limit cycle near [Image: see text] (solid lines in (a,b)). Parameter values are (δ, m) = (0.00055, 0.0005) for (a,b) and (δ, m) = (0.001, 0.0005) for (c,d). Other parameter values are σ = 1, κ = 1.69 yr1, β = 280 yr1, μ = 1/50 yr1 and γ = 365/22 yr1.
Figure 4.

Figure 4.

( a ) Stability regions…

Figure 4.

( a ) Stability regions of [Image: see text] (bottom-left region) and [Image:…

Figure 4.
(a) Stability regions of [Image: see text] (bottom-left region) and [Image: see text] (upper-right region) at (δ, m) = (0.001, 0.0005) in the bistability region of figure 2, as they depend on D and σ, and with x(0) = 0.8. Other parameter values are κ = 1.69 yr1, β = 280 yr1, μ = 1/50 yr1 and γ = 365/22 yr1. (b) Simulated vaccine coverage with a scare period of D = 3 years for σ = 1 in the stability region of [Image: see text] (grey line), σ = 5 in the stability region of [Image: see text] (dashed line) and σ = 10 in the stability region of [Image: see text] (solid black line). Other parameter values are δ = 0.001, m = 0.0005, κ = 1.69 yr1, β = 280 yr1, μ = 1/50 yr1 and γ = 365/22 yr1.
Figure 5.

Figure 5.

( a ) Stability regions…

Figure 5.

( a ) Stability regions of [Image: see text] (bottom-right region) and [Image:…

Figure 5.
(a) Stability regions of [Image: see text] (bottom-right region) and [Image: see text] (upper-left region) at (δ, m) = (0.001, 0.0005) in the bistability region of figure 2, as they depend on κ and x(0). (b) Simulated vaccine coverage for κ = 2 yr1 in the stability region of [Image: see text] (dashed line) and κ = 3 yr1 in the stability region of [Image: see text] (solid line). Other parameter values are σ = 1, δ = 0.001, m = 0.0005, x(0) = 0.6, β = 280 yr1, μ = 1/50 yr1 and γ = 365/22 yr1.
Figure 6.

Figure 6.

Simulation of pertussis vaccine coverage…

Figure 6.

Simulation of pertussis vaccine coverage in the UK in the period 1967–2010, at…

Figure 6.
Simulation of pertussis vaccine coverage in the UK in the period 1967–2010, at the estimated parameter values (σ = 26.1, δ = 1.95 × 104, m = 8.43 × 105, D = 5.89 years and κ = 1.69 yr1) used to generate figure 1e,f, which correspond to the vaccine scare (solid line), and for the same parameter values, but with no scare having ever occurred, σ = 1 (dashed line). Other parameter values are β = 280 yr1, μ = 1/50 yr1 and γ = 365/22 yr1.

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