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

Figure 1

Solution of delayed SIR model (3.2), when 𝑟=0.1, 𝛽=0.1, 𝜎=0.05, 𝑎=0.5, 𝛼=0.5, 𝛿=0.1, and time-lag 𝜏=1 when 𝑆^∗=20, 𝐾=40, ℛ₀=2, ℛ_𝑐=2.33 (a) and 𝐾=80, ℛ₀=4, ℛ_𝑐=2.33 (b) that display periodic outbreak of the disease. We get a stable solution when 1<ℛ₀≤ℛ_𝑐 and a stable periodic solution when ℛ₀>ℛ_𝑐.

(a)

(b)