Dynamical Behavior of a New Epidemiological Model

Figure 1

When 𝜏=0, 𝑏=6, 𝛼=𝑑=𝑘=1, 𝑐=4, and 𝑢₁=𝑢₂=2, then 𝑅₀=0.8571<1. Taking the initial value (3,1,1), then the solution (𝑆(𝑡),𝐼(𝑡),𝐷(𝑡)) approaches to the disease-free equilibrium 𝐸₀=(6,0,0) as 𝑡→∞.