The Assessment of the Arising of Food Allergy among Antiacid Users Using Mathematical Model

Author(s)
Hyun Mo Yang,
Ariana Campos Yang,
Keity Souza Santos,
Clovis Eduardo Galvão,
Fabio Fernandes Morato Castro

Affiliation(s)

UNICAMP-IMECC-DMA, Pra?a Sérgio Buarque de Holanda, Campinas, Brazil.

Division of Allergy, Clinics Hospital of FM-USP, S?o Paulo, Brazil.

UNICAMP-IMECC-DMA, Pra?a Sérgio Buarque de Holanda, Campinas, Brazil.

Division of Allergy, Clinics Hospital of FM-USP, S?o Paulo, Brazil.

ABSTRACT

The first case of a new food allergy, an anaphylactic reaction to Manioc (Manihot esculenta or Manihot utilissima), also called cassava and tapioca, was described in 2001. Cassava is a tuber widely consumed in Brazil, which has been consumed by native Indians, i.e., more than 500 years ago, so why are the first cases just emerging now? We address this question by developing a mathematical model considering the fact that proton pump inhibitors (PPIs) for digestive disorders maintain the cassava allergen intact due to the elevation in pH of gastric juice, thereby facilitating its presentation to the immune system. The model assumed the mass action law including saturation to describe the recruitment of PPIs users, and Hill function to describe the sensitization of immune system by the allergens and the acquisition of full food allergy. Analytical results were obtained from the model, and numerical simulations were done. The estimated period of time elapsed since the introduction of antiacids before the diagnosis of food allergy was 15 years. The food allergy may become a public health problem, if PPIs are being used indiscriminately and irregularly. The results obtained from the analysis of the model suggest that the use of nonprescription antiacids, like PPIs, may be recommended or approved by the physician in order to avoid the rising of food allergy.

The first case of a new food allergy, an anaphylactic reaction to Manioc (Manihot esculenta or Manihot utilissima), also called cassava and tapioca, was described in 2001. Cassava is a tuber widely consumed in Brazil, which has been consumed by native Indians, i.e., more than 500 years ago, so why are the first cases just emerging now? We address this question by developing a mathematical model considering the fact that proton pump inhibitors (PPIs) for digestive disorders maintain the cassava allergen intact due to the elevation in pH of gastric juice, thereby facilitating its presentation to the immune system. The model assumed the mass action law including saturation to describe the recruitment of PPIs users, and Hill function to describe the sensitization of immune system by the allergens and the acquisition of full food allergy. Analytical results were obtained from the model, and numerical simulations were done. The estimated period of time elapsed since the introduction of antiacids before the diagnosis of food allergy was 15 years. The food allergy may become a public health problem, if PPIs are being used indiscriminately and irregularly. The results obtained from the analysis of the model suggest that the use of nonprescription antiacids, like PPIs, may be recommended or approved by the physician in order to avoid the rising of food allergy.

Cite this paper

H. Yang, A. Yang, K. Santos, C. Galvão and F. Castro, "The Assessment of the Arising of Food Allergy among Antiacid Users Using Mathematical Model,"*Applied Mathematics*, Vol. 3 No. 3, 2012, pp. 293-307. doi: 10.4236/am.2012.33045.

H. Yang, A. Yang, K. Santos, C. Galvão and F. Castro, "The Assessment of the Arising of Food Allergy among Antiacid Users Using Mathematical Model,"

References

[1] R. Chiron, “Anaphylactic Reaction to Tapioca,” Journal of Allergy and Clinical Immunology, Vol. 107, No. 2, 2001, pp. S270-S271.

[2] C. E. S. Galv?o, L. K. Iwai, M. E. B. Andrade, J. Kalil and F. F. M. Castro, “Latex Allergy and Cross-Reactivity to Manioc: Report of 2 Cases,” Journal of Allergy and Clinical Immunology, Vol. 113, No. 2, 2004, pp. 144.

[3] A. Gaspar, C. Neto-Braga, G. Pires, R. Murta, M. Morais-Almeida and J. Rosado-Pinto, “Anaphylactic Reaction to Manioc: Cross-reactivity to Latex,” Allergy, Vol. 58, No. 7, 2003, pp. 683-684. doi:10.1034/j.1398-9995.2003.00184.x

[4] M. Ibero, M. J. Castillo and F. Pineda, “Allergy to Cassava: A New Allergenic Food with Cross-reactivity to Latex,” Journal of Investigational Allergology and Clinical Immunology, Vol. 17, No. 6, 2007, pp. 409-412.

[5] K. Ishizaka, T. Ishizaka and M. M. Hornbrook, “Physico-Chemical Properties of Human Reaginic Antibody. IV. Presence of a Unique Immunoglobulin as a Carrier of Reaginic Activity,” Journal of Immunology, Vol. 97, No. 1, 1966, pp. 75-85.

[6] K. S. Santos, C. E. Galv?o, V. M. F. Resende, C. O. Martins, E. Vejvar, G. Gadermaier, F. Ferreira, J. Kalil and F. F. M. Castro, “Identification of New Brazilian Allergens from Manioc Manihot esculenta,” Abstract Book of Food Allergy and Anaphylaxis Meeting, Venice, 2011.

[7] I. Pali-Scholl and E. Jensen-Jarolim, “Anti-Acid Medication as a Risk Factor for Food Allergy,” Allergy, Vol. 66, No. 4, 2011, pp. 469-477. doi:10.1111/j.1398-9995.2010.02511.x

[8] K. S. Santos, C. D. Galvao, G. Gadermaier, V. M. F. Resende, C. O. Martins, D. S. Misumi, A. C. Yang, F. Ferreira, M. S. Palma, J. Kalil and F. F. M. Castro, “Allergic Reactions to Manioc (Manihot esculenta Crantz): Identification of Novel Allergens with Potential Involvement in Latex-fruit Syndrome,” Journal of Allergy and Clinical Immunology, Vol. 128, No. 6, 2011, pp. 13671369. doi:10.1016/j.jaci.2011.07.019

[9] V. N. Uversky, J. R. Gillespie and A. L. Fink, “Why Are ‘Natively Unfolded’ Proteins Unstructured under Physiologic Conditions?” Proteins: Structure, Function, and Genetics, Vol. 41, No. 3, 2000, pp. 415-427. doi:10.1002/1097-0134(20001115)41:3<415::AID-PROT130>3.0.CO;2-7

[10] J. M. Mullin, M. C. Valenzano, M. Whitby, D. Lurie, J. D. Schmidt, V. Jain, O. Tully, K. Kearney, D. Lazowick, G. Mercogliano and J. J. Thornton, “Esomeprazole Induces Upper Gastrointestinal Tract Transmucosal Permeability Increase,” Alimentary Pharmacology & Therapeutics, Vol. 28, No. 11-12, 2008, pp. 1317-1325. doi:10.1111/j.1365-2036.2008.03824.x

[11] L. J. Murray, M. Gabello, D. S. Rudolph, C. P. Farrell, M. Morgan, A. P. Martin, J. C. Underwood, M. C. Valenzano and J. M. Mullin, “Transmucosal Gastric Leak Induced by Proton Pump Inhibitors,” Digestive Diseases and Sciences, Vol. 54, No. 7, 2009, pp. 1408-1417. doi:10.1007/s10620-008-0528-z

[12] C. K. Ching and S. K. Lam, “Antiacids. Indications and Limitations,” Drugs, Vol. 47, No. 2, 1994, pp. 305-317. doi:10.2165/00003495-199447020-00006

[13] F. Halter, “Clinical Use of Antiacids,” Journal of Physiology and Pharmacology, Vol. 44, No. 3, 1993, pp. 6174.

[14] J. G. Penston and R. E. Pounder, “A Survey of Dyspepsia in Great Britain,” Alimentary Pharmacology & Therapeutics, Vol. 10, 1996, pp. 8-9.

[15] A. P. Corder, R. H. Jones, G. H. M. Sadler, P. Daniels and C. D. Johnson, “Heartburn, Oesophagitis and Barrett’s Oesophagus in Self-medicating Patients in General Practice,” British Journal of Clinical Practice, Vol. 50, No. 5, 1996, pp. 245-248.

[16] K. Furu and B. Straume, “Use of Antiacids in a General Population: The Impact of Health-Related Variables, Lifestyle and Sociodemographic Characteristics,” Journal of Clinical Epidemiology, Vol. 52, No. 6, 1999, pp. 509-516. doi:10.1016/S0895-4356(99)00020-7

[17] J. Isolauri and P. Laippala, “Prevalence of Symptoms Suggestive of Gastrooesophageal Reflux Disease in an Adult Population,” Annals of Medicine, Vol. 27, No. 1, 1995, pp. 67-70. doi:10.3109/07853899509031939

[18] N. F. Adkinson, J. W. Yunginger, W. W. Busse, B. S. Bocher, S. T. Holgate and F. E. R. Simons, “Middleton’s Allergy: Principles & Practice,” Mosby Inc., Philadelphia, 2003. doi:10.1016/j.jtbi.2010.10.013

[19] F. Grob, G. Metzner and U. Behn, “Mathematical Modeling of Allergy and Specific Immunotherapy: Th1-Th2Treg Interactions,” Journal of Theoretical Biology, Vol. 269, No. 1, 2011, pp. 70-78.

[20] H. M. Yang, “Mathematical Modeling of Solid Cancer Growth with Angiogenesis,” Theoretical Biology and Medical Modelling, Vol. 9, No. 2, 2012.

[21] J. D. Murray, “Mathematical Biology,” Spinger-Verlag, New York, 1989.

[22] C. B. Madsen, S. Hattersley, J. Buck, S. M. Gendel, G. F. Houben, J. O. B. Hourihane, A. Mackie, E. N. C. Mills, P. N? rhede, S. L. Taylor and R. W. R. Crevel, “Approaches to Risk Assessment in Food Allergy: Report from a Workshop Developing a Framework for Assessing the Risk from Allergenic Foods,” Food and Chemical Toxicology, Vol. 47, No. 2, 2009, pp. 48-89. doi:10.1016/j.fct.2008.12.001

[23] A. V. Hill, “The Possible Effects of The Aggregation of The Molecules of Haemoglobin on its Dissociation Curves,” The Journal of Physiology, Vol. 40, 1910, pp. iv-vii.

[24] K. Furu and B. Straume, “Changes in Antiacid Use over a 9-year Period in a General Population Adjusted for Changes in Dyspeptic Complaints,” Norsk Epidemiologi, Vol. 18, No. 2, 2008, pp. 201-207.

[25] W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, “Numerical Recipes. The Arts of Scientifc Computing (FORTRAN Version),” Cambridge University Press, Cambridge, 1989.

[26] D. Karlsson, S. Karlsson, E. Gustafsson, B. H. Normarkc and P. Nilsson, “Modeling The Regulation of The Competence-Evoking Quorum Sensing Network in Streptococcus pneumoniae,” BioSystems, Vol. 90, No. 1, 2007, pp. 21-23. doi:10.1016/j.biosystems.2006.08.005

[27] M. B. F. Leite, R. C. Bassanezi and H. M. Yang, “The Basic Reproduction Ratio for a Model of Directly Transmitted Infections Considering the Virus Charge and the Immunological Response,” IMA Journal of Mathematics Applied in Medicine and Biology, Vol. 17, No. 1, 2000, pp. 15-31. doi:10.1093/imammb/17.1.15

[28] L. Esteva and H. M. Yang, “Mathematical Model to Assess the Control of Aedes aegypti Mosquitoes by The Sterile Insect Technique,” Mathematical Biosciences, Vol. 198, No. 2, 2005, pp. 132-147. doi:10.1016/j.mbs.2005.06.004

[29] G. H. Golub and C. F. van Loan, “Matrix Computations,” The Johns Hopkins University Press, Baltimore, 1996.

[30] J. K. Hale, “Ordinary Differential Equations,” John Wiley and Sons, New York, 1969.

[1] R. Chiron, “Anaphylactic Reaction to Tapioca,” Journal of Allergy and Clinical Immunology, Vol. 107, No. 2, 2001, pp. S270-S271.

[2] C. E. S. Galv?o, L. K. Iwai, M. E. B. Andrade, J. Kalil and F. F. M. Castro, “Latex Allergy and Cross-Reactivity to Manioc: Report of 2 Cases,” Journal of Allergy and Clinical Immunology, Vol. 113, No. 2, 2004, pp. 144.

[3] A. Gaspar, C. Neto-Braga, G. Pires, R. Murta, M. Morais-Almeida and J. Rosado-Pinto, “Anaphylactic Reaction to Manioc: Cross-reactivity to Latex,” Allergy, Vol. 58, No. 7, 2003, pp. 683-684. doi:10.1034/j.1398-9995.2003.00184.x

[4] M. Ibero, M. J. Castillo and F. Pineda, “Allergy to Cassava: A New Allergenic Food with Cross-reactivity to Latex,” Journal of Investigational Allergology and Clinical Immunology, Vol. 17, No. 6, 2007, pp. 409-412.

[5] K. Ishizaka, T. Ishizaka and M. M. Hornbrook, “Physico-Chemical Properties of Human Reaginic Antibody. IV. Presence of a Unique Immunoglobulin as a Carrier of Reaginic Activity,” Journal of Immunology, Vol. 97, No. 1, 1966, pp. 75-85.

[6] K. S. Santos, C. E. Galv?o, V. M. F. Resende, C. O. Martins, E. Vejvar, G. Gadermaier, F. Ferreira, J. Kalil and F. F. M. Castro, “Identification of New Brazilian Allergens from Manioc Manihot esculenta,” Abstract Book of Food Allergy and Anaphylaxis Meeting, Venice, 2011.

[7] I. Pali-Scholl and E. Jensen-Jarolim, “Anti-Acid Medication as a Risk Factor for Food Allergy,” Allergy, Vol. 66, No. 4, 2011, pp. 469-477. doi:10.1111/j.1398-9995.2010.02511.x

[8] K. S. Santos, C. D. Galvao, G. Gadermaier, V. M. F. Resende, C. O. Martins, D. S. Misumi, A. C. Yang, F. Ferreira, M. S. Palma, J. Kalil and F. F. M. Castro, “Allergic Reactions to Manioc (Manihot esculenta Crantz): Identification of Novel Allergens with Potential Involvement in Latex-fruit Syndrome,” Journal of Allergy and Clinical Immunology, Vol. 128, No. 6, 2011, pp. 13671369. doi:10.1016/j.jaci.2011.07.019

[9] V. N. Uversky, J. R. Gillespie and A. L. Fink, “Why Are ‘Natively Unfolded’ Proteins Unstructured under Physiologic Conditions?” Proteins: Structure, Function, and Genetics, Vol. 41, No. 3, 2000, pp. 415-427. doi:10.1002/1097-0134(20001115)41:3<415::AID-PROT130>3.0.CO;2-7

[10] J. M. Mullin, M. C. Valenzano, M. Whitby, D. Lurie, J. D. Schmidt, V. Jain, O. Tully, K. Kearney, D. Lazowick, G. Mercogliano and J. J. Thornton, “Esomeprazole Induces Upper Gastrointestinal Tract Transmucosal Permeability Increase,” Alimentary Pharmacology & Therapeutics, Vol. 28, No. 11-12, 2008, pp. 1317-1325. doi:10.1111/j.1365-2036.2008.03824.x

[11] L. J. Murray, M. Gabello, D. S. Rudolph, C. P. Farrell, M. Morgan, A. P. Martin, J. C. Underwood, M. C. Valenzano and J. M. Mullin, “Transmucosal Gastric Leak Induced by Proton Pump Inhibitors,” Digestive Diseases and Sciences, Vol. 54, No. 7, 2009, pp. 1408-1417. doi:10.1007/s10620-008-0528-z

[12] C. K. Ching and S. K. Lam, “Antiacids. Indications and Limitations,” Drugs, Vol. 47, No. 2, 1994, pp. 305-317. doi:10.2165/00003495-199447020-00006

[13] F. Halter, “Clinical Use of Antiacids,” Journal of Physiology and Pharmacology, Vol. 44, No. 3, 1993, pp. 6174.

[14] J. G. Penston and R. E. Pounder, “A Survey of Dyspepsia in Great Britain,” Alimentary Pharmacology & Therapeutics, Vol. 10, 1996, pp. 8-9.

[15] A. P. Corder, R. H. Jones, G. H. M. Sadler, P. Daniels and C. D. Johnson, “Heartburn, Oesophagitis and Barrett’s Oesophagus in Self-medicating Patients in General Practice,” British Journal of Clinical Practice, Vol. 50, No. 5, 1996, pp. 245-248.

[16] K. Furu and B. Straume, “Use of Antiacids in a General Population: The Impact of Health-Related Variables, Lifestyle and Sociodemographic Characteristics,” Journal of Clinical Epidemiology, Vol. 52, No. 6, 1999, pp. 509-516. doi:10.1016/S0895-4356(99)00020-7

[17] J. Isolauri and P. Laippala, “Prevalence of Symptoms Suggestive of Gastrooesophageal Reflux Disease in an Adult Population,” Annals of Medicine, Vol. 27, No. 1, 1995, pp. 67-70. doi:10.3109/07853899509031939

[18] N. F. Adkinson, J. W. Yunginger, W. W. Busse, B. S. Bocher, S. T. Holgate and F. E. R. Simons, “Middleton’s Allergy: Principles & Practice,” Mosby Inc., Philadelphia, 2003. doi:10.1016/j.jtbi.2010.10.013

[19] F. Grob, G. Metzner and U. Behn, “Mathematical Modeling of Allergy and Specific Immunotherapy: Th1-Th2Treg Interactions,” Journal of Theoretical Biology, Vol. 269, No. 1, 2011, pp. 70-78.

[20] H. M. Yang, “Mathematical Modeling of Solid Cancer Growth with Angiogenesis,” Theoretical Biology and Medical Modelling, Vol. 9, No. 2, 2012.

[21] J. D. Murray, “Mathematical Biology,” Spinger-Verlag, New York, 1989.

[22] C. B. Madsen, S. Hattersley, J. Buck, S. M. Gendel, G. F. Houben, J. O. B. Hourihane, A. Mackie, E. N. C. Mills, P. N? rhede, S. L. Taylor and R. W. R. Crevel, “Approaches to Risk Assessment in Food Allergy: Report from a Workshop Developing a Framework for Assessing the Risk from Allergenic Foods,” Food and Chemical Toxicology, Vol. 47, No. 2, 2009, pp. 48-89. doi:10.1016/j.fct.2008.12.001

[23] A. V. Hill, “The Possible Effects of The Aggregation of The Molecules of Haemoglobin on its Dissociation Curves,” The Journal of Physiology, Vol. 40, 1910, pp. iv-vii.

[24] K. Furu and B. Straume, “Changes in Antiacid Use over a 9-year Period in a General Population Adjusted for Changes in Dyspeptic Complaints,” Norsk Epidemiologi, Vol. 18, No. 2, 2008, pp. 201-207.

[25] W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, “Numerical Recipes. The Arts of Scientifc Computing (FORTRAN Version),” Cambridge University Press, Cambridge, 1989.

[26] D. Karlsson, S. Karlsson, E. Gustafsson, B. H. Normarkc and P. Nilsson, “Modeling The Regulation of The Competence-Evoking Quorum Sensing Network in Streptococcus pneumoniae,” BioSystems, Vol. 90, No. 1, 2007, pp. 21-23. doi:10.1016/j.biosystems.2006.08.005

[27] M. B. F. Leite, R. C. Bassanezi and H. M. Yang, “The Basic Reproduction Ratio for a Model of Directly Transmitted Infections Considering the Virus Charge and the Immunological Response,” IMA Journal of Mathematics Applied in Medicine and Biology, Vol. 17, No. 1, 2000, pp. 15-31. doi:10.1093/imammb/17.1.15

[28] L. Esteva and H. M. Yang, “Mathematical Model to Assess the Control of Aedes aegypti Mosquitoes by The Sterile Insect Technique,” Mathematical Biosciences, Vol. 198, No. 2, 2005, pp. 132-147. doi:10.1016/j.mbs.2005.06.004

[29] G. H. Golub and C. F. van Loan, “Matrix Computations,” The Johns Hopkins University Press, Baltimore, 1996.

[30] J. K. Hale, “Ordinary Differential Equations,” John Wiley and Sons, New York, 1969.