Disease Control through Voluntary Vaccination Decisions Based on the Smoothed Best Response

Figure 4

Bifurcation diagrams showing the equilibrium structure of system (1). Except as described below, the parameters used here are as follows: 𝐴=0.5, 𝛽=0.25, 𝑞=0.9, 𝑑=0.15, 𝑟=0.08, 𝑘=2, 𝛼=0.01, and 𝜙=0.12. With these parameters, ℛ₀=0.8786. (a) 𝜙, the proportion of susceptible individuals who are faced with the decision of whether or not to be vaccinated per unit time, is varied from 0 to 0.25; (b) 𝛼, the perceived cost of taking the vaccination, is varied from 0 to 1; (c) 𝑘, the degree of rationality, is varied from 0.01 to 10⁴.

(a)

(b)

(c)