Abstract
Malaria is a serious disease with a high developing in the world. It still major public health problem. In 2008, 109 countries were declared as endemic to the disease, 243 million malaria cases were reported causing nearly a million of death, primarily of children under 5 year; nearly 3000 children die every day in Africa. In Brazil, Amazonia is the area that presents the highest number of cases and consequently having many cases of morbidity and mortality, especially when we deal with the Malaria caused by the Plasmodium falciparum. The parasite in the human organism attacks liver cells and erythrocytes. Plasmodium falciparum is the deadliest protozoan because attacks a high number of erythrocytes at any evolutionary phase, making the person susceptible to others disease. The human immune system (HIS) operates in the invasion of this parasite (innate system) and during its development in the organism (adaptive system), it is responsible for finding and neutralizing cells that are infected to prevent their proliferation, avoiding the disease or the death of the patient. The complex biology of Plasmodium falciparum and its interaction with the HIS are the motivation of this work. Therefore, with mathematical models and computer simulations which have been growing considerably in the medical science area, this work presents a model to contribute quickly and trustfully for this interaction. The mathematical modeling used is structured by non-linear ordinary differential equations of first-order that describes the action of the HIS to eliminate the protozoa. We have performed several simulations to investigate the behavior of the protozoa front of the human organism without the action of the HIS, and the results were compared to the behavior with the action of the HIS.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Yang, H.M.: Comparison between Shistosomiasis Transmission Modelling Considering Acquired Immunity and Age-structured Contact Pattern with Infested Water. Math. Biosc. 184, 1–26 (2003)
Barrozo, S., Yang, H.M.: Desenvolvimento de um modelo para resposta imunlógica primária célula-mediada. Tendências em Matemática Aplicada e Computacional. 7(1), 31–41 (2006)
Chitnis, C.E., Blackman, M.J.: Host cell invasion by malaria parasites. Parasitology Today 16, 411–415 (2000)
Da Silva-Nunes, M., Ferreira, M.U.: Clinical spectrum of uncomplicated malaria ub senu-immune Amazonians: beyond the “symptomatic” VS “asymptomatic” dichotomy. Mem. Inst. Oswaldo Cruz 102, 341–347 (2007)
World Health Organization. Severe falciparum malaria. Transactions of the Royal Society of Tropical Medicine and Hygiene 94(supl. 1), S1/1–S1/90 (2000)
Cooke, B.M., Wahlgren, M., Coppel, R.L.: Falciparum malaria: sticking-up, standing out and outstanding. Parasitology Today 16, 416–420 (2000)
Vieira, P.P., Ferreira, M.U., Alecrim, M.G., Alecrim, W.D., Da Silva, L.H., et al.: pfcrtpolymorphism and the spread of chloroquine resistance in Plasmodium falciparum populations across the Amazon Basin. Infect. Dis. 190, 417–424 (2004)
Bezzi, M., Celada, F., Ruffo, S., Seiden, P.E.: The transition between immune and disease states in a cellular automaton model of clonal immune response. Physica A: Statistical and Theoretical Physics 245(1-2), 145–163 (1997)
Sompayrac, L.M.: How the Immune System Works. Wiley, John & Sons (2008) (incorporated)
Janeway, C., Murphy, K.P., Travers, P., Walport, M., Janeway, C.: Immunobiology, 5th edn. Garland Science, New York (2001)
Edelstein-Keshet, L.: Mathematical Models in Biology, New York. Birkhauser Mathematics Series (1988)
Zorzeno, R.M.S., Pinho, S.T.R., Ferreira, C.P., da Silva, P.C.A.: On the study of the dynamic aspects of parasitemia in the blood cycle of malaria. Europen Physcial J. Special Topics 143, 125–134 (2007)
Molineaux, L., Diebner, H.H., Eichner, M., Collins, W.E., Jeffery, G.M., Dietz, K.: Parasitology 122, 379–391 (2001)
Adams, J.H., Blair, P.L., Kaneko, O., Peterson, D.S.: An expanding ebl family of Plasmodium falciparum. Trends Parasitol 17(6), 297–299 (2001)
Al-Yaman, F., Genton, B., Anders, R., Taraika, J., Ginny, M., Mellor, S., Alpers, M.P.: Assessment of the role of the humoral response to Plasmodium falciparum MSP2 compared to RESA and SPf66 in protecting Papua New Guinean children from clinical malaria. Parasite Immunol. 17(9), 493–501 (1995)
Anders, R.F., Smythe, J.A.: Polymorphic antigens in Plasmodium falciparum. Blood 74(6), 1865–1875 (1989)
Aribot, G., Rogier, C., Sarthou, J., Trape, J., Balde, A., Druilhe, P., Roussilhon, C.: Pattern of immunoglobulin isotype response to Plasmodium falciparum blood-stage antigens in individuals living in a holoendemic area of Senegal (Dielmo, west Africa). Am. J. Trop. Med. Hyg. 54(5), 449–457 (1996)
Artavanis-Tsakonas, K., Riley, E.M.: Innate immune response to malaria: rapid induction of IFN-gamma from human NK cells by live Plsmodium falciparum- infected erythrocytes. J. Immunol. 169(6), 2956–2963 (2002)
Ayi, K., Turrini, F., Piga, A., Arese, P.: Enhanced phagocytosis of ring-parasitized mutant erythrocytes: a common mechanism that explain protection against falciparum malaria in sickle trait and beta-thalassemia trait. Blood 104(10), 3364–3371 (2004)
Babiker, H., Ranford-Cartwright, L., Currie, D., Charlwood, J., Billingsley, P., Teuscher, T., Walliker, D.: Random mating in a natural population of the malaria parasite Plasmodium falciparum. Parasitology 109 (pt 4), 413–421 (1994)
Bachmann, A., Predehl, S., May, J., Harder, S., Burchard, G.D., Gilberger, T.W., Tannich, E., Bruchhaus, I.: Highly co-ordinated var gene expression and switching in clinical Plasmodium falciparum isolates from non-immune malaria patients. Cell Microbiol. 13(9), 1397–1409 (2011)
Butcher, J.C.: The Numerical Analysis of Ordinary Diferential Equations. John Wiley and Sons Inc., NY (1987)
Dormand, J.R.: Numerical Methods for Diferential Equations, A Computational Approach. CRC Press, NY (1996)
Hildebrand, F.B.: Finite-Difference Equations and Simulations, Section 2.2. Prentice-Hall, Englewood Cliffs (1968)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lima de Oliveira, C.H. et al. (2012). Mathematical Implementation of Interaction between Malaria and Immune System. In: Coello Coello, C.A., Greensmith, J., Krasnogor, N., Liò, P., Nicosia, G., Pavone, M. (eds) Artificial Immune Systems. ICARIS 2012. Lecture Notes in Computer Science, vol 7597. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33757-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-33757-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33756-7
Online ISBN: 978-3-642-33757-4
eBook Packages: Computer ScienceComputer Science (R0)