Dynamical Analysis of SIR Epidemic Models with Distributed Delay

Figure 2

Illustration of basic behavior of system (7) on the threshold values 𝑅=1.44>1, where Λ=1.8,𝜇=0.2,𝛽=0.08,𝑟=0.3,𝑎=0.1, the initial value is (𝑆₀,𝐼₀,𝑍₀)=(0.7,0.3,0.3), and 𝐸^∗=(6.25,1.1,6.25).

(a)   Time series of 𝑆(𝑡),𝐼(𝑡),𝑍(𝑡)

(b) Phase portrait of 𝑆(𝑡),𝐼(𝑡)

(c) Phase portrait of 𝑆(𝑡),𝑍(𝑡)

(d) Phase portrait of 𝐼(𝑡),𝑍(𝑡)

(e) Phase portrait of 𝑆(𝑡),𝐼(𝑡),𝑍(𝑡)