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

Figure 5

(a) Simulated results of the best-response systems (18) and (19) for 𝐴=0.5, 𝛽=0.23, 𝑞=0.9, 𝑑=0.13, 𝑟=0.08, 𝜙=0.1, and 𝛼=0.01. With these parameters, the basic reproduction number of models (18) and (19) are ℛ_𝐵𝑝0=0.7083 and ℛ_𝐵𝑛0=1.2532, respectively. Since 𝛼<𝐴𝛽/((𝑟+𝑑)(𝐴/𝑑)^𝑞)−𝑑=0.0329, the epidemic dynamics switch between models (18) and (19) until an endemic equilibrium is reached. (b) Simulated results of system (1) for 𝑘=2 with all the other parametric values are the same as (a). Since the basic reproduction number ℛ₀=0.9076, the disease free equilibrium 𝐸₀ of model (1) is stable.

(a)

(b)