Abstract: We considered a class of dynamic model of human immunodeficiency virus (HIV) transmission and proposed a class of HIV transmission dynamic system by using the rule of population transmission in epidemic contagion region. Firstly, using the functional homotopic mapping method, we obtained the sequence of approximate solutions of a class of HIV nonlinear transmission dynamic system and their  uniformly convergence, and gave an example to get all the approximate solutions. Then the quantitative and qualitative analysis of the solution for HIV transmission dynamic system was carried out. The results show that the expressions of approximate solution can regulate the distribution for the number of infected persons and susceptible persons.

Key words: approximate solution,  human groups for HIV transmission, nonlinear dynamic model, homotopic mapping