Volatile opinions in vaccinating behaviour: analysis using geometric singular perturbation theory

Abstract

In the age of social media, decision dynamics are facilitated by the social networks, which allow real-time spread of information and accelerate changes of opinions. These phenomena has an impact on individuals behaviour in response to an epidemic, for example in vaccination campaign. In particular, opinions mutate faster than the spread of epidemics. Hence, we propose an SIR model with voluntary vaccination choices evolving on two time scales. We assume that opinion switching depends on the incidence of the disease. We apply Geometrical Singular Perturbation Theory (GSPT) to such a model and we then compare the geometric analysis with the Quasi-Steady State Approximation (QSSA) approach, showing a criticality in the latter. Later, we apply the GSPT approach to the model already studied in Della Marca and d’Onofrio (2021) via the QSSA approach by considering medium-large values of the strategy switching parameter.