# American Institute of Mathematical Sciences

May  2002, 2(2): 257-264. doi: 10.3934/dcdsb.2002.2.257

## A model for an SI disease in an age - structured population

 1 Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

Received  May 2001 Revised  October 2001 Published  February 2002

We formulate and analyze a model for an infectious disease which does not cause death but for which infectives remain infective for life. We derive the basic reproductive number $R_0$ and show that there is a unique globally asymptotically stable equilibrium, namely the disease - free equilibrium if $R_0 < 1$ and the endemic equilibrium if $R_0 > 1$. However, the relation between the basic reproductive number, the mean age at infection, and the mean life span depends on the distribution of life spans and may be quite different from that for exponentially distributed life spans or very short infective periods.
Citation: Fred Brauer. A model for an SI disease in an age - structured population. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257
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