Mathematical modeling of the immune system response to pathogens

The detection and elimination of pathogens in an organism are the main tasks of its immune system. The most important cells involved in these processes are neutrophils and macrophages. These processes might have two resolutions: The first is the possibility of pathogen elimination, and the other the possibility of the inflammation resolution. In this work, we present several mathematical models involving immune cell densities and inflammation levels. Our general goal is to exhibit the possible pathogen eradication or the inflammation resolution. We use bifurcation techniques in order to analyze how parameter variations may change the system evolution. Our results indicate that the elimination of apoptotic neutrophils by macrophages has a dichotomy effect: It contributes to the decrease of the inflammation level, but it may hinder the pathogen elimination. Also, an increment of the average neutrophil life can improve healthy outcomes. Moreover, we find scenarios when pathogens cannot be eliminated, as well as conditions for their successful eradication.