Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate

Figure 2

Solution of delayed SIR model (3.2), when 𝑟=0.1, 𝐾=50, 𝛽=0.1, 𝜎=0.005, 𝑎=0.5, 𝛼=0.5, 𝛿=0.1, 𝑆^∗=10.5, ℛ₀=4.7>ℛ_𝑐=3 with time-lag 𝜏=0.01<𝜏^∗ (a) and 𝜏=𝜏^∗=0.58 (b) that display periodic outbreak of the disease due to a Hopf bifurcation when 𝜏=𝜏^∗.

(a)

(b)