Yakubovich’s oscillatority of circadian oscillations models

The interplay of public intervention and private choices in determining the outcome of vaccination programmes

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.

The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach

When the incidence and prevalence of most common vaccine preventable childhood infectious diseases are constantly low, as is the case in many industrialized countries, the incidence of vaccine-associated side effects might become a key determinant in vaccine demand. We study an SIR transmission model with dynamic vaccine demand based on an imitation mechanism where the perceived risk of vaccination is modelled as a function of the incidence of vaccine side effects. The model shows some important differences compared to previous game dynamic models of vaccination, and allows noteworthy inferences as regards both the past and future lifetime of vaccination programmes. In particular it is suggested that a huge disproportion between the perceived risk of disease and vaccination is necessary in order to achieve high coverages. This disproportion is further increased in highly industrialised countries. Such considerations represent serious challenges for future vaccination programmes.