Effect of transport and competition on ligand binding

Dynamic analysis of a parasite population model

We study the dynamics of a model that describes the competitive interaction between an invading species (a parasite) and its antibodies in an living being. This model was recently used to examine the dynamical competition between Tripanosoma cruzi and its antibodies during the acute phase of Chagas' disease. Depending on the antibody properties, the model yields three types of outcomes, corresponding, respectively, to healing, chronic disease, and host death. Here, we study the dynamics of the parasite-antibody interaction with the help of simulations, obtaining phase trajectories and phase diagrams for the system. We show that, under certain conditions, the size of the parasite inoculation can be crucial for the infection outcome and that a retardation in the stimulated production of an antibody species may result in the parasite gaining a definitive advantage. We also find a criterion for the relative sizes of the parameters that are required if parasite-generated decoys are indeed to help the invasion. Decoys may also induce a qualitatively different outcome: a limit cycle for the antibody-parasite population phase trajectories.

A simple model for the interaction between T. cruzi and its antibodies during Chagas infection

The evolution of the acute phase of the Chagas infection is analysed from the viewpoint of the dynamic competition between parasite and antibody populations. A simple model for the growth and annihilation of these populations is shown to provide a suitable description of the experimental data. We also find that it is possible to classify antibody response to Trypanosoma cruzi, into three main cases, defined by antibody efficiency, initial number and creation rate. The model clearly indicates the most relevant parameters determining the evolution of the Chagas infection, yielding a simple asymptotic criterion for the host survival.