A geometric analysis of the impact of large but finite switching rates on vaccination evolutionary games

• Published in: Nonlinear analysis: real world applications Vol. 75; p. 103986
• Main Authors: Della Marca, Rossella, d’Onofrio, Alberto, Sensi, Mattia, Sottile, Sara
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2024; Elsevier
• Subjects: Behavioural epidemiology of infectious diseases; Entry–exit function; Fast–slow system; Geometric singular perturbation theory; Mathematical epidemiology; Mathematics; Vaccine hesitancy; Mathematical epidemiology; Entry–exit function; Fast–slow system; Geometric singular perturbation theory; Vaccine hesitancy; Behavioural epidemiology of infectious diseases; vaccine hesitancy; entry-exit function; mathematical epidemiology; geometric singular perturbation theory; fast-slow system behavioural epidemiology of infectious diseases entry-exit function vaccine hesitancy mathematical epidemiology geometric singular perturbation theory; behavioural epidemiology of infectious diseases; fast-slow system
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2023.103986

In contemporary society, social networks accelerate decision dynamics causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases by means of vaccines. This means that opinion dynamics can nowadays be much faster than the spread of epidemics. Hence, we propose a Susceptible–Infectious–Removed epidemic model coupled with an evolutionary vaccination game embedding the public health system efforts to increase vaccine uptake. This results in a global system “epidemic model + evolutionary game”. The epidemiological novelty of this work is that we assume that the switching to the strategy “pro vaccine” depends on the incidence of the disease. As a consequence of the above-mentioned accelerated decisions, the dynamics of the system acts on two different scales: a fast scale for the vaccine decisions and a slower scale for the spread of the disease. Another, and more methodological, element of novelty is that we apply Geometrical Singular Perturbation Theory (GSPT) to such a two-scale 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 disease prevalence-based model already studied in (Della Marca and d’Onofrio, Comm Nonl Sci Num Sim, 2021) via the QSSA approach by considering medium–large values of the strategy switching parameter. •We propose a SIR model paired to a Vaccine EvoGame driven by Disease Incidence.•The system has two time-scales: fast for vaccine decisions and slow for disease spread.•Geometrical Singular Perturbation Theory (GSPT) and Quasi Steady State Approximation (QSSA) are used to study the model.•The finiteness vs unboundedness of the strategy switching rate remarkably impacts on the system dynamics.•The case in which the EvoGame is driven by Disease Prevalence is also studied by means of GSPT.