Abstract
An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency is assumed a function of the 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 the application of the theorem is also given. Model analysis and simulations show that complacency resulting from dependence of HIV transmission on the number of AIDS cases in a community leads to damped periodic oscillations in the number of infective 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.
Highlights
Complacency is used to mean to “relax” or “revert” to high risk sexual behaviours such as multiple sexual partners, sex with prostitutes and non-condom use once the HIV prevalence reduces to very low levels, with the number of AIDS cases becoming less in the community
We show that complacency could lead to periodic behavior of the HIV/AIDS epidemic
This may not translate into oscillations in HIV prevalence since the susceptible population size is assumed to keep increasing at low prevalence levels and the period of the oscillations is of the order of several years
Summary
Complacency is used to mean to “relax” or “revert” to high risk sexual behaviours such as multiple sexual partners, sex with prostitutes and non-condom use once the HIV prevalence reduces to very low levels, with the number of AIDS cases becoming less in the community. It is assumed that behaviour change depends on the number of AIDS patients (HIV infected persons with fully blown AIDS symptoms) in the community. Treatment of AIDS patients could lead to periodicity of the HIV epidemic with resurgences in number of new HIV infections.
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