The interplay of public intervention and private choices in determining the outcome of vaccination programmes
- PMID:23049682
- PMCID: PMC3462214
- DOI: 10.1371/journal.pone.0045653
The interplay of public intervention and private choices in determining the outcome of vaccination programmes
Abstract
After a long period of stagnation, traditionally explained by the voluntary nature of the programme, a considerable increase in routine measles vaccine uptake has been recently observed in Italy after a set of public interventions aiming to promote MMR immunization, whilst retaining its voluntary aspect. To account for this take-off in coverage we propose a simple SIR transmission model with vaccination choice, where, unlike similar works, vaccinating behaviour spreads not only through the diffusion of "private" information spontaneously circulating among parents of children to be vaccinated, which we call imitation, but also through public information communicated by the public health authorities. We show that public intervention has a stabilising role which is able to reduce the strength of imitation-induced oscillations, to allow disease elimination, and to even make the disease-free equilibrium where everyone is vaccinated globally attractive. The available Italian data are used to evaluate the main behavioural parameters, showing that the proposed model seems to provide a much more plausible behavioural explanation of the observed take-off of uptake of vaccine against measles than models based on pure imitation alone.
Conflict of interest statement
Figures

calibrated on Italian uptake of vaccine against measles in 2008; second row:I-model (
) with endemic coverage
calibrated on Italian uptake of vaccine against measles in 1996; (c) third row:I-model with endemic coverage
calibrated on Italian uptake of vaccine against measles in 2008; bottom row: the basic SIR model with constant coverage
. The figure reports time trends of the Effective Reproduction Number
(left column), the infective fraction
(centre), the vaccinated proportion
(right column). Other parameter values:
,
,
year
,
day
. Initial conditions are:
.
set to achieve
(Italian measles coverage in 2003); second row:
set to achieve
(Italian measles coverage in 2008); third row:
set to achieve elimination with
(WHO target for measles elimination); bottom row:
set to achieve thePVE
. The figure reports time trends of the: Effective Reproduction Number
(left column), infective fraction
(centre), vaccinated proportion
(right column). Other parameter values:
,
,
year
,
day
. Initial conditions:
.
,
,
year
,
day
.
set at its pre-1996 level of 0.56; (b) theI-model, with
reduced in order to allow an equilibrium uptake of 90%; (c) theG-model with
set at the pre-1996 level and
set in order to allow an equilibrium uptake of 90%; (d) theG-model with
allowing an equilibrium uptake of 95%. The four models are initialised at 1996 after 20 years of steady dynamics implied by model (a). A flat line at the level
is also added for reference. The four panels are drawn for
= 2.5 (North-West),
= 3.0 (North-East),
= 3.5 (South-West),
= 4.0 (South-East). All the four models are initialised from the endemic state of model (a):
.References
- Reluga TC, Bauch CT, Galvani AP (2006) Evolving public perceptions and stability in vaccine uptake. Math Biosci 204: 185–198. - PubMed
- d’Onofrio A, Manfredi P, Salinelli E (2007) Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases. Theor Popul Biol 71: 301–317. - PubMed
- d’Onofrio A, Manfredi P, Poletti P (2011) The impact of vaccine side effects on the natural history of vaccination programmes. J Theor Biol 273: 63–71. - PubMed
- d’Onofrio A, Manfredi P, Salinelli E (2008) Fatal SIR diseases and rational exemption to vaccina-tion. Math Med Biol 25: 337–357. - PubMed
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