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. 2002 Nov-Dec:180:29-48.
doi: 10.1016/s0025-5564(02)00108-6.

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

P van den Driessche  1 , James Watmough
Affiliations

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

P van den Driessche et al. Math Biosci. 2002 Nov-Dec.

Abstract

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 equilibria for R0 near one. This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.

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