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.
Highlights
Complacency is used to mean to “relax” or “revert” to high risk sexual behaviours such as multiple sex partners, sex with prostitutes and non-condom use once the HIV prevalence reduces to very low levels and the number of AIDS cases become rare in the community
Complacency is used in the context of a community that has registered significant decreases in HIV prevalence
In the case of HIV/AIDS, damped oscillations have been shown by Simwa and Pokhariyal [15] using back calculation methods to derive incidence estimates from annual AIDS case reports for Kenya and Uganda
Summary
Complacency is used to mean to “relax” or “revert” to high risk sexual behaviours such as multiple sex partners, sex with prostitutes and non-condom use once the HIV prevalence reduces to very low levels and the number of AIDS cases become rare 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. This dependence has been alluded to by a number of authors such as Leaman and Bhupal [7] and Okware et al [8]. In the case of HIV/AIDS, damped oscillations have been shown by Simwa and Pokhariyal [15] using back calculation methods to derive incidence estimates from annual AIDS case reports for Kenya and Uganda Their incidence curves show recurrent behaviour with damped oscillations. Ignoring safer sex messages when condoms are effective in preventing HIV but other sexually transmitted infections and unwanted pregnancies has been described as “misplaced” and the stigma attached to HIV/AIDS as “a great enemy” [7]
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