Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.
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.
van den Driessche
P
P
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4. pvdd@math.uvic.ca
Watmough
James
J
D000818:Animals; D018562:Disease Transmission, Infectious; D019353:Endemic Diseases; D004812:Epidemiologic Methods; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical