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

Figure 2

Simulated phase portraits of system (1) for 𝐴=0.5, 𝛽=0.25, 𝑞=0.9, 𝑑=0.1, 𝛼=0.01, 𝑟=0.1, and 𝑘=2, projected on the 𝑆−𝐼 plane (a, c) and on the 𝑅−𝑉 plane (b, d). For (a) and (b), 𝜙=0.15. Since ℛ₀=0.84, the disease free equilibrium 𝐸₀ is stable. For (c) and (d), 𝜙 has been decreased to 0.05 causing ℛ₀ to increase to 1.18. Since ℛ₀>1, the disease free equilibrium 𝐸₀ is unstable and the endemic equilibrium 𝐸₁ exists and is stable.

(a)

(b)

(c)

(d)