Geometric singular perturbation theory analysis of an epidemic model with spontaneous human behavioral change

• Published in: Journal of mathematical biology Vol. 82; no. 6; p. 54
• Main Author: Schecter, Stephen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Behavior; Biological Evolution; Differential equations; Epidemic models; Epidemics; Game Theory; Humans; Mathematical and Computational Biology; Mathematical models; Mathematics; Mathematics and Statistics; Models, Biological; Perturbation theory; Singular perturbation; Social interactions; Imitation dynamics; 92D30; 91A22; Entry–exit function; Geometric singular perturbation theory; Epidemiological modeling; Evolutionary game theory; 34E15
• ISSN: 0303-6812; 1432-1416; 1432-1416
• DOI: 10.1007/s00285-021-01605-2

We consider a model due to Piero Poletti and collaborators that adds spontaneous human behavioral change to the standard SIR epidemic model. In its simplest form, the Poletti model adds one differential equation, motivated by evolutionary game theory, to the SIR model. The new equation describes the evolution of a variable x that represents the fraction of the population following normal behavior. The remaining fraction 1 - x uses altered behavior such as staying home, social isolation, mask wearing, etc. Normal behavior offers a higher payoff when the number of infectives is low; altered behavior offers a higher payoff when the number is high. We show that the entry–exit function of geometric singular perturbation theory can be used to analyze the model in the limit in which behavior changes on a much faster time scale than that of the epidemic. In particular, behavior does not change as soon as a different behavior has a higher payoff; current behavior is sticky. The delay until behavior changes is predicted by the entry–exit function.