Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment

Figure 1

The figure of infective sizes at equilibria versus 𝑅₀ when 𝐼₀=30, 𝐴=80, 𝛽₁=0.01, 𝛽₂=0.01, 𝛾=0.01, 𝑑=0.9, 𝜖=0.01, 𝑟=1, 𝑝₀=1.6782, 𝑝₁=1.541, 𝑝₂=1.7074, where (i) of Theorem 2.2 holds. The bifurcation from the disease-free equilibrium at 𝑅₀=1 is forward, and there is a backward bifurcation from an endemic equilibrium at 𝑅₀=1, which leads to the existence of multiple endemic equilibria.