Abstract
In this paper, we derive and analyse a delayed $SI$ model with saturated incidence rate and latent or infectious period $\tau$. We prove local stability of the system's steady states in the absence and the presence of the time delay. We discover the the disease-free steady state is locally asymptotically stable if $\mathcal{R}_0 1$. While, the endemic steady state is always stable for any parameter values and for all $\tau\ge0$.
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