The symbiosis (Sym) and pathogenesis (Pat) is a duality problem of microbial infection, including HIV/AIDS. Statistical analysis of inequalities and duality in gene coexpression networks (GCNs) of HIV-1 infection may gain novel insights into AIDS. In this study, we focused on analysis of GCNs of uninfected subjects and HIV-1-infected patients at three different stages of viral infection based on data deposited in the GEO database of NCBI. The inequalities and duality in these GCNs were analyzed by the combination of the double-connectivity (DC) approach and the Gini's method. DC analysis reveals that there are significant differences between positive and negative connectivity in HIV-1 stage-specific GCNs. The inequality measures of negative connectivity and edge weight are changed more significantly than those of positive connectivity and edge weight in GCNs from the HIV-1 uninfected to the AIDS stages. With the permutation test method, we identified a set of genes with significant changes in the inequality and duality measure of edge weight. Functional analysis shows that these genes are highly enriched for the immune system, which plays an essential role in the Sym-Pat duality (SPD) of microbial infections. Understanding of the SPD problems of HIV-1 infection may provide novel intervention strategies for AIDS.