Analysis of a Delayed SIR Epidemic Model

An SIR epidemic model with incubation time and saturated incidence rate is formulated, where the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the infective. Threshold quantity R₀ is derived which determines whether the disease dies out or remains endemic. If R₀ <; 1, the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears. If R₀ > 1, there will be an endemic and the disease is permanent if it initially exists.