Mathematical Modeling of the Chagasic Trypanosomiasis

Abstract

In this paper, we show an extended model that describes the dynamic interaction between the immune response of a mammal and Trypanosoma cruzi parasite during the acute phase of a Chagas Disease. The model considers the immune and cellular response, plus the different stages (intracellular and extracellular) of T. cruzi inside of a mammal host. The analysis of the time evolution of populations is made obtaining phase diagrams to determine the stability of the steady states in terms of its parameters. The system gives two steady states, which are associated with the Healing and Chronic state of the disease. The dead case obtained before when only the humoral immune response is considered it gets disappeared. The fundamental implication of this result is the benefit that the cellular immune response produces for the host as for the parasite since it allows to extend the life of the host while extending the critical state of the disease without destroying the habitat of the parasite.

Keywords

Chagas Disease, Mathematical Model, Immune Response, Trypanosoma cruzi

Author Biography

Shirlene Patricia Vega

Biographical summary
Ph.D. Shirlene Vega
Researcher Professor

C.C. 49784712

I hold a Bachelor degree in Math and Physics Education given by Universidad Popular del Cesar (Valledupar-Cesar) in 1999. Later I started my master studies in physics finished in 2004 at Puerto Rico University in Mayaguez campus, some years after I began my Ph.D. studies in Argentina, where I received the degree in 2014 from  Universidad Nacional de Córdoba de la Facultad de Matemática, Astronomía y Física.

I have worked in several colleges, in Colombia and abroad among which I can name: Universidad Pedagógica y Tecnológica de Colombia (Duitama campus), Universidad de Puerto Rico (Mayaguez campus), Universidad Nacional de Córdoba (Argentina), Universidad Pontificia Bolivariana (Medellín) and as bilingual math teacher at Plainfield High School in the state of New Jersey (United States). Currently, I am working as a researcher professor at Universidad Católica Luis Amigó, member of the research group Sistemas de la Información y Sociedad del Conocimiento and, part-time professor in the Physics Institute at Universidad de Antioquia both in Medellín.

In the last years, I have worked in projects related to physics teaching and the mathematical modeling of biological systems, specifically to the interaction between the Trypanosoma cruzi parasite (the causing agent of Chagas disease) and the mammal's immune response.  Among the articles published so far I have: Who benefits from cellular immune response during Chagas disease? (Biosystems, 2018), Modelling Parasite Reduction Mechanisms in Chagas Disease. (Journal of Biological Systems, 2015), y Can We Heal Chagas Infection? ( Journal of Theoretical Biology, 2014) and some others. 

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