Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.

@article{Driessche2002ReproductionNA,
  title={Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.},
  author={Pauline van den Driessche and James Watmough},
  journal={Mathematical biosciences},
  year={2002},
  volume={180},
  pages={29-48}
}
A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic… CONTINUE READING
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