The purpose of this paper is to select a model for HIV that uses few parameters while fitting the world prevalence and death data well. Here we consider a set of models based on Erlang's method of stages, including some with and some without social distancing. The use of stages is supported by biological studies which suggest that HIV passes through stages in each individual, although the exact number is not known. This set of models can represent such stages using a successive number of classes. To perform model selection, we compute R 0 and use it to estimate initial values of the parameters in this model. We run thousands of iterations of a Nelder-Mead simplex search algorithm to determine the optimal values of parameters for each model and the error associated with each model. These errors are used to compute AIC c values and then the AIC c values are compared to select the most likely model. The selected model from this experiment contains the social distancing term as well as four infected classes/stages. We then perform identifiability analysis and determine that the "true values" of the parameters for this model are uniquely determinable based on the data points.

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Twenty hemophiliacs were infected with Korean subclade B (KSB) of HIV-1 from two cash-paid plasma donors in Korea in 1990. Our previous studies revealed that Korean red ginseng (KRG) intake increases the frequency of gross deletion in the nef gene (gDeltanef). We investigated whether KRG and highly active antiretroviral therapy (HAART) affected the frequency of gDeltanef in the 20 hemophiliacs who share common characteristics of the HIV-1 source, mode of transmission, and infection time. Over a 10-year period, we obtained 522 nef amplicons by nested PCR using 172 samples of peripheral blood mononuclear cells. Of the 522 nef amplicons, 69 (13.2%) were gDeltanef. Despite a 2-fold higher monthly dose of KRG, the frequency of gDeltanef detection (3.2%) was significantly reduced during HAART compared with that prior to HAART (20.6%) (p < 0.001). gDeltanef was detected significantly more in patients treated with a monthly KRG intake of more than 60 g (26.8%) than in patients treated with a monthly KRG intake of less than 60 g (10.5%) (p < 0.05). These finding suggest that the frequency of gDeltanef is dependent on the amount of KRG intake, although further study is needed. These data might provide a new perspective on the pathogenesis of HIV-1.