Mathematical Modeling of the Chagasic Trypanosomiasis
![](https://revistas.uptc.edu.co/public/journals/20/cover_issue_625_es_ES.jpg)
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.
References
[1] Organización Panamericana de la Salud, . Estimación cuantitativa de la enfermedad de Chagas en las Américas. Montevideo, Uruguay: Organización Panamericana de la Salud, 2006
[2] Federación Médica Colombiana, “Enfermedad de Chagas, Memorias” Ministerio de Salud yProtección Social, 2012. [Online]. Available: https://www.minsalud.gov.co/sites/rid/Lists/BibliotecaDigital/RIDE/VS/TH/Memorias
chagas.pdf. [Accessed: 23-May-2019].
[3] Canals, M., Cáceres, D., Alvarado, S., Canals, A., Cattan P.E., 2017. Modeling Chagas disease in Chile: From vector to congenital transmission.Biosystems 156-157, 63-71.
[4] Martorano Raimundo, S., Massad, E., Yang, H.M., 2010. Modelling congenital transmission of Chagas disease. Biosystems 99, 215-222.
[5] Storino, R., Milei, J., 1994. Patología, in: Storino,R., Milei, J., (Eds.), Enfermedad de Chagas. Mosby Doyma, Buenos Aires, pp. 141-184.
[6] Storino, R., 1998. Enfermedad de Chagas, in: Mautner B y col. Medicina. Centro Editor Fundación Favaloro, Buenos Aires, Cap 25: 774-783.
[7] Goldsby, R.A., Kindt, T.J., Osborne, B.A.,Kuby, J., 2000. Immunology, fourth ed., WH
Freeman & Co, Gordondsville, VA.
[8] Regueiro, J.R., Lopez-Larrea, C., González- Rodríguez, S., Martínez-Noves, E., 2010. Inmunology:
Biology and Pathology of the Immune System, fourth ed., Médica Panamericana, Buenos Aires, Argentina.
[9] Delves, P.J., Seamus, J.M., Roitt, I.M., 2017. Immunology. Essentials, thirteenth ed. Wiley-
Blackwell, Oxford, UK.
[10] Tarleton, R.L., 1990. Depletion of CD8+ T cells increases susceptibility and reverses vaccine-induced immunity in mice infected with Trypanosoma cruzi. J. Immunol. 144(2), 717-24.
[11] Tarleton, R.L., Grusby, M.J., Postan, M., Glimcher, L.H., 1996. Trypanosoma cruzi infection in MHC-deficient mice: further evidence for the role of both class I and class II-restricted T cells in immune resistance and disease. Int.
Immunol. 8(1), 13-22.
[12] Rottenberg, M.E., Bakhiet, M., Olsson, T., Kristensson, K., Mak, T., Wigzell, H., Orn, A., 1993. Differential susceptibilities of mice genomically deleted of CD4 and CD8 to infections with Trypanosoma cruzi or Trypanosoma brucei. Infect. Immun. 61, 5129- 5133.
[13] Rottenberg, M.E., Riarte, A., Sporrong, L., Altcheh, J., Petray, P., Ruiz, A.M., Wigzell, H., Orn, A., 1995. Outcome of infection with differentstrains of Trypanosoma cruzi in mice lacking CD4 and/or CD8. Immunol. Lett. 45(1-
2), 53-60.
[14] Sibona, G.J., Condat, C.A., Cossy Isasi, S., 2005. Dynamics of the antibody - T. cruzi competition
during Chagas infection: Prognostic relevance of intracellular replication. Physical Review E 71, 020901(R).
[15] Vega, S.P., Sibona, G.J., Condat, C.A., 2012. Curing by infecting: two strain competition during the acute phase of Chagas disease, in Mondaini, R.P. (Ed.), Biomat 2011 International Symposium on Mathematical and Computational Biology. World Scientific Publishing Co., Singapore, pp. 297-308.
[16] Vega-Royero, S.P., Sibona, G.J. 2014. Can we heal Chagas infection? Journal of Theoretical Biology 340, 23-29.
[17] Basso, B., Moretti, E., Fretes, R. 2008. Vaccination with epimastigotes of different strains
of Trypanosoma rangeli protects mice against Trypanosoma cruzi infection Memórias do Instituto Oswaldo Cruz 103(4), 370-374.
[18] Condat, C.A., Cossy Isasi, S., Sibona, G.J., 2003. Parasite-Antibody Competition in Chagas Disease. Comments on Theoretical Biology 8, 587-607.
[19] EL Bouhdidi, A., Truyens, C., Rivera, M.T., Bazin, H., Carlier, I., 1994. Trypanosoma cruzi infection in mice induces a polyisotypic hypergammaglobulinaemia and parasite-specific response involving high IgG2a concentrations and highly avid IgG1 antibodies. Parasite Immunol. 16, 69-76.
[20] Cossy Isasi, S., Condat, C.A., Sibona, G.J., 2009. Why does GM1 induce a potent beneficial response to experimental Chagas disease HSFP Journal 3, 142-151.
[21] Cossy Isasi, S., Sibona, G.J., Condat, C.A., 2001. A Simple Model for the Interaction Between T. cruzi and its Antibodies During Chagas Infection. J. Theor. Biol. 208, 1-13.
[22] Sibona, G.J., Condat, C.A., 2002. Dynamics analysis of a parasite population model. Phys. Rev. E 65, 031918.
[23] Vega, S.P., Sibona, G.J., Condat, C.A., Curing by infecting: two-strain competition during the acute phase of Chagas disease, in Mondaini R (ed.), Proceedings 11th International Symposium on Mathematical and Computational Biology, World Scientific, Singapore, pp:296-308, 2011.
[24] Yang, H.M., 2015. A mathematical model to assess the immune response against Trypanosoma cruzi infection. Journal of Biological Systems. 23(1), 131-163.
[25] Murray, J.D., (2002) Mathematical Biology, third ed., Springer, New York.
[26] Vega-Royero, S.P., Sibona, G.J., Who benefits from cellular immune response during the Chagas disease Biosystems 171, 66-7.
[27] Sanchez Alberti A et al., 2017. Engineered trivalent immunogen adjuvanted with a STING agonist confers protection against Trypanosoma cruzi infection. npj Vaccines 2(1), 9.
[28] Urton, G., Von Hagen, A., 2015. Encyclopedia of the Incas. Rowman & Littlefield, London,
pp.156.