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Global stability of a delayed SIR epidemic model with density dependent birth and death rates. (English) Zbl 1105.92034
Summary: An SIR epidemic model with density dependent birth and death rates is formulated. In our model it is assumed that the total number of the population is governed by a logistic equation. The transmission of infection is assumed to be of the standard form, namely proportional to $I\left(t-h\right)/N\left(t-h\right)$ where $N\left(t\right)$ is the total (variable) population size, $I\left(t\right)$ is the size of the infective population and a time delay $h$ is a fixed time during which the infectious agents develops in the vector. We consider transmission dynamics for the model. Stability of an endemic equilibrium is investigated. The stability result is stated in terms of a threshold parameter, that is, a basic reproduction number ${R}_{0}$.
##### MSC:
 92D30 Epidemiology 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations