Rossella Della Marca

University of Parma

Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to ‘pseudo–rational’ behaviours: parents overweigh real and imaginary side effects of vaccines and do not fully perceive the actual risks linked to the disease. Nonetheless, the Public Health Systems may enact control strategies, such as awareness campaigns, to favour vaccine propensity.
The complex dynamics leading to vaccine uptake has been modelled as an imitation game (d’Onofrio et al., PLoS ONE, 2012) or, equivalently, as ‘infection of ideas’ (Wang et al., Phys. Rep., 2016), augmented by terms modelling the switching of vaccine strategy (vaccination vs not vaccination) in the case where the abovementioned campaign is enacted.
Here we investigate the noteworthy case, of great relevance in the age of social network, where the decision speed is rapid, so that a quasi–steady–state approximation can be applied to the SIR-like model proposed in (d’Onofrio et al., PLoS ONE, 2012). This allows us to infer and analyze a new behavioural epidemiology model that is nonlinear in the control. Then, we search for the optimal time-profiles of vaccine awareness campaigns, with the aim of minimizing the total costs of the disease spread and control. Such cost is formed by different ’sub–costs’: that related to the disease burden, the vaccination costs and the economic burden to enact the campaigns.
We numerically face the problem through both deterministic and stochastic optimization algorithms. In the latter case, we also provide a statistical assessment of the obtained solutions.

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