A Competition Model Applied to a Chagas’ Infection: Two parasite Strains and One Specie of Antibody

VEGA SHIRLENE, SIBONA GUSTAVO, CONDAT CARLOS Y COSSI ISSASI

Workshop; Workshop on Mathematical methods and modeling of biophysical phenomena I; 2011

IMPA- Instituto Nacional de Matematica Pura E Aplicada.

A  Competition Model Applied to a Chagas’ Infection: Two parasite Strains and One Specie of Antibody   We have extended the analysis of our model for the acute phase of Chagas’ disease studying the competition between two parasite strains and one antibody species. The main result is the nonexistence of an equilibrium among the immune system and both strains at the same time, result that indicates an indirect competition between the strains to survive the antibodies attack. As a result of its dynamics, the model yields six possible outcomes that can be grouped into three main cases: healing, chronic disease and host death; each case subdivided into two considering which is the survival strain. The results are presented as phase trajectories and phase diagrams. They show that, under certain conditions, the size of the strain parasite inoculation is fundamental for the infection outcome. Our results agree with many of the reported clinical observations: which have not found in any hemocultural test the coexistence of both strains of the Trypanosoma Cruzi (agent causing of the Chagas’ Disease) in carrying organisms. Moreover this indicates that a similar, but not so infective strain can be use for vaccination.