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

Figure 3

The logarithm logℛ₀ of the basic reproduction number of system (1). Except as described below, the parameters used here are as follows: 𝐴=0.5, 𝛽=0.25, 𝑞=0.9, 𝑑=0.1, 𝑟=0.1, 𝑘=2, 𝛼=0.1, and 𝜙=0.1. logℛ₀ is shown (a) when the degree of rationality 𝑘 is increased from 0 to 6 and the perceived cost of vaccination 𝛼 is varied from 0 to 0.15; (b) when the decision rate 𝜙 is varied from 0.09 to 0.11 and 𝛼 is varied from 0 to 0.1; (c) when the incidence rate 𝛽 is varied from 0.2 to 0.3 and 𝛼 is varied from 0 to 0.2; (d) when 𝛽 is varied from 0.2 to 0.3 and 𝜙 is varied from 0.09 to 0.11. The solid curve in each panel denotes the points where the basic reproduction number ℛ₀ is equal to 1 (i.e., logℛ₀=0). The disease-free equilibrium is stable for parameter values corresponding to points under these curves and unstable for those above for (a), (b), and (c) and the opposite holds for (d). The column on the right-hand side of each panel gives the color coding for different values of logℛ₀.

(a)

(b)

(c)

(d)