Computational and Mathematical Methods in Medicine
Volume 7 (2006), Issue 1, Pages 27-35
doi:10.1080/10273660600890057

Mathematical Model for HIV/AIDS with Complacency in a Population with Declining Prevalence

F. Baryarama, J. Y. T. Mugisha, and L. S. Luboobi

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.

Abstract

An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency is assumed a function of number of AIDS cases in a community with an inverse relation. A method to find the equilibrium state of the model is given by proving a stated theorem. An example to illustrate use of the theorem is also given. Model analysis and simulations show that complacency resulting from dependence of HIV transmission on number of AIDS cases in a community leads to damped periodic oscillations in the number of infectives with oscillations more marked at lower rates of progression to AIDS. The implications of these results to public health with respect to monitoring the HIV/AIDS epidemic and widespread use of antiretroviral (ARV) drugs is discussed.