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hiv epi - American Journal of Infectious Diseases 1(1 55-60...

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American Journal of Infectious Diseases 1 (1): 55-60, 2005 ISSN 1553-6203 © 2005 Science Publications Corresponding Author: Flugentius Baryarama, Department of Mathematics, Makerere University, Box 7062, Kampala, Uganda 55 Periodicity of the HIV/AIDS Epidemic in a Mathematical Model that Incorporates Complacency Flugentius Baryarama, Livingstone S. Luboobi and Joseph Y.T. Mugisha Department of Mathematics, Makerere University, Box 7062, Kampala, Uganda 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. Key words: HIV/AIDS, periodicity, mathematical model, complacency INTRODUCTION 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. Complacency is used in the context of a community that has registered significant decreases in HIV prevalence. This is the case for most Ugandan communities. Uganda has registered decreasing HIV prevalence since the early 1990s both nationally and based on community studies of selected high risk sub- populations [1-6] . To model complacency, 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] . Recurrent behaviour is a key feature of most epidemics including nutrition related epidemics such as Kwashiorkor and Pellagra. A report on an investigation on the pellagra disease in Kulto, Angola showed annual epidemics of the disease with major outbreaks in June to September associated with the maize harvesting season [9] . Clearly the observed periodicity was due to seasonal variations. A number of diseases show such seasonal variations for a number of reasons including school calendars, weather conditions and behaviours in response to such seasonal events. Infectious diseases like measles, tuberculosis, typhus fever, influenza, chicken pox and several sexually transmitted diseases have been documented to show recurrent outbreaks that are less dependent on seasonal variations. It is unlikely that HIV/AIDS would exhibit seasonal variations
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