Dynamical Analysis of SIR Epidemic Models with Distributed Delay

Figure 3

Illustration of basic behavior of system (9) on the threshold values ℜ=0.4155<1, where Λ=1,𝜇=0.2,𝛽=0.5,𝑟=0.6,𝑎=3,𝑇=1, and 𝛿=0.8.

(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)