Computational and Mathematical Methods in Medicine
Volume 7 (2006), Issue 1, Pages 15-26

A Mathematical Model for the Dynamics of HIV/AIDS with Gradual Behaviour Change

Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda

Received 20 April 2006; Revised 11 May 2006; Accepted 5 June 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An HIV/AIDS model that incorporates gradual behaviour change is formulated with a variable force of infection for the adult population. The variability is modelled using a general function of time since introduction of the initial infective and exemplified for three specific functions. Expressions for the time taken for the reproductive number to reduce to unity and expressions for the time taken to attain a stationary steady state are deduced and discussed. Model projections for urban, peri-urban and rural Uganda are compared with corresponding antenatal clinic sites prevalence trends. The analysis shows that the dramatic decline in HIV prevalence in Uganda in the early 1990s was only possible through drastic declines in the force of infection. Since prevalence was high and reductions in frequency of sexual acts was minimal, the huge reduction could be attributed to reductions in probability of transmission per sexual act probably due to increased selective condom use among high risk sexual partnerships since overall condom use was low.