Using computer algebra, the respiratory infection of the histoplasma capsulatum fungus was modeled and analyzed; the effects of the infection could also be described as a change in the lungs capacity to expand (associated with its elastic modulus). A further analysis to the immune system was also done in order to describe and model the way the body can handle those kinds of infections once they are hosted in the body. Using those models we can describe the behavior of the respiratory infection and then how to reduce or control its effects. As an investigation in the medical field, we need to test the models obtained and compare the results with the real infection behavior. The models where made based on the diffusive-convective equation; giving some initial and boundary conditions, we can get to the results obtained, which can describe how the infection is spreading and with a previous study of the immune system, the infection control done by the body can also be modeled.