| Abstract: | A precise definition of the basic reproduction number,
, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if
, then the disease free equilibrium is locally asymptotically stable; whereas if
, then it is unstable. Thus,
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
near one. This criterion, together with the definition of
, 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. |
