The effect of density-dependent treatment and behavior change on the dynamics of HIV transmission

In this work, we propose a model for heterosexual transmission of HIV/AIDS in a population of varying size with an intervention program in which treat ment and/or behavior change of the infecteds occur as an increasing functio n of the density of the infected class in the population. This assumption h as socio-economic implications which is important for public health conside rations since density-dependent treatment/behavior change may be more cost- saving than a program where treatment/behavior change occurs linearly with respect to the number of infecteds. We will make use of the conservation la w of total sexual contacts which enables us to reduce the two-sex model to a simpler one-sex formulation. Analytical results will be given. Unlike a s imilar model With linear treatment/behavior change in Hsieh (1996) where co nditions were obtained for the eradication of disease, we will show that de nsity-dependent treatment/behavior change cannot eradicate the disease if t he disease is able to persist without any treatment/behavior change. This w ork demonstrates the need to further understand how treatment/behavior chan ge occurs in a society with varying population.