Threshold dynamics of a periodic SIR model with delay in an infected compartment
2015
Threshold dynamics of epidemic models in periodic environments
attract more attention. But there are few papers which are concerned
with the case where the infected compartments satisfy a delay
differential equation. For this reason, we investigate the dynamical
behavior of a periodic SIR model with delay in an infected
compartment. We first introduce the basic reproduction number
$\mathcal {R}_0$ for the model, and then show that it can act as a
threshold parameter that determines the uniform persistence or
extinction of the disease. Numerical simulations are performed to
confirm the analytical results and illustrate the dependence of
$\mathcal {R}_0$ on the seasonality and the latent period.
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