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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Mathematical Modeling for Asthma due to Air Pollution

Journal of Applied Nonlinear Dynamics 10(2) (2021) 219--228 | DOI:10.5890/JAND.2021.06.003

Nita H. Shah , Ankush H. Suthar, Purvi M. Pandya

Department of Mathematics, Gujarat University, Ahmedabad -- 380009, Gujarat, India

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Abstract

The human~respiratory~and~cardiovascular~systems get affected from surrounding atmosphere. Systematic study of indoor and outdoor pollution is needed for better understanding of their global epidemiology. In this substantial body of research, a mathematical model for transmission of asthma in a variable size population under the effects of indoor smoke and outdoor air pollution is proposed. In addition, the reproduction number for the dynamical system is formulated which signifies the intensity of asthma exacerbation. The global and local stability of acquired equilibrium points is studied. The performance of the model is simulated numerically which illustrates how polluted environment effectively increases levels of aeroallergens and their effect on asthma exacerbation, and how such exposures can be meaningfully reduced.

Acknowledgments

Authors thank anonymous reviewers for their constructive comments. Ankush Suthar is funded by a Junior Research Fellowship from the Council of Scientific & Industrial Research (file no.-09/070(0061)/2019-EMR-I) and all the authors are thankful to DST-FIST file {\#} MSI-097 for technical support to the Department of Mathematics, Gujarat University.

References

  1. [1]  Martinez, F.D. (2007), Genes, environments, development and asthma: a reappraisal, European Respiratory Journal, 29(1), 179-184.
  2. [2]  Cohen, A.J., Brauer, M., Burnett, R., Anderson, H.R., Frostad, J., Estep, K., Balakrishnan, K., Brunekreef, B., Dandona, L., Dandona, R., and Feigin, V. (2017), Estimates and 25-year trends of the global burden of disease attributable to ambient air pollution: an analysis of data from the Global Burden of Diseases Study 2015, The Lancet, 389(10082), 1907-1918.
  3. [3]  World Health Organization. Air pollution. 2018 [accessed 2018 Dec 18]. Available from: \underline {https://www.who.int/airpollution/en/}.
  4. [4]  Landrigan, P.J., Fuller, R., Fisher, S., Suk, W.A., Sly, P., Chiles, T.C., and Bose-OReilly, S. (2019), Pollution and childrens health. Science of The Total Environment, 650, 2389-2394.
  5. [5]  Hansel, N.N., Romero, K.M., Pollard, S.L., Bose, S., Psoter, K.J., Underhill, L., Johnson, C., Williams, D.A., Curriero, F.C., Breysse, P., and Koehler, K. (2019), Ambient Air Pollution and Variation in Multiple Domains of Asthma Morbidity among Peruvian Children, Annals of the American Thoracic Society, 16(3), 348-355.
  6. [6]  Lim, H., Kwon, H.J., Lim, J.A., Choi, J.H., Ha, M., Hwang, S.S., and Choi, W.J. (2016), Short-term effect of fine particulate matter on childrens hospital admissions and emergency department visits for asthma: a systematic review and meta-analysis, Journal of Preventive Medicine and Public Health, 49(4), 205-219.
  7. [7]  Strickland, M.J., Darrow, L.A., Klein, M., Flanders, W.D., Sarnat, J.A., Waller, L.A., Sarnat, S.E., Mulholland, J.A., and Tolbert, P.E. (2010), Short-term associations between ambient air pollutants and pediatric asthma emergency department visits, American journal of respiratory and critical care medicine, 182(3), 307-316.
  8. [8]  Damato, G., Liccardi, G., and DAmato, M. (2000), Environmental risk factors (outdoor air pollution and climatic changes) and increased trend of respiratory allergy, Journal of investigational allergology {$\&$ clinical immunology}, 10(3), 123-128.
  9. [9]  Whittle, E., Leonard, M.O., Gant, T.W., and Tonge, D.P. (2019), Multi-Method Molecular Characterisation of Human Dust-Mite-associated Allergic Asthma, Scientific Reports, 9(1), 8912-8930.
  10. [10]  Annesi-Maesano, I., Baiz, N., Banerjee, S., Rudnai, P., Rive, S., and SINPHONIE Group. (2013), Indoor air quality and sources in schools and related health effects, Journal of Toxicology and Environmental Health, Part B, 16(8), 491-550.
  11. [11]  Dockery, D.W. and Stone, P.H. (2007), Cardiovascular risks from fine particulate air pollution.
  12. [12]  Boezen, H.M., van der Zee, S.C., Postma, D.S., Vonk, J.M., Gerritsen, J., Hoek, G., Brunekreef, B., Rijcken, B., and Schouten, J.P. (1999), Effects of ambient air pollution on upper and lower respiratory symptoms and peak expiratory flow in children, The lancet, 353(9156), 874-878.
  13. [13]  Epton, M.J., Dawson, R.D., Brooks, W.M., Kingham, S., Aberkane, T., Cavanagh, J.A.E., Frampton, C.M., Hewitt, T., Cook, J.M., McLeod, S., and McCartin, F. (2008), The effect of ambient air pollution on respiratory health of school children: a panel study, Environmental Health, 7(1), 16.
  14. [14]  Gauderman, W.J., Vora, H., McConnell, R., Berhane, K., Gilliland, F., Thomas, D., Lurmann, F., Avol, E., Kunzli, N., Jerrett, M., and Peters, J. (2007), Effect of exposure to traffic on lung development from 10 to 18 years of age: a cohort study, The Lancet, 369(9561), 571-577.
  15. [15]  Hajat, S., Haines, A., Goubet, S.A., Atkinson, R.W., and Anderson, H.R. (1999), Association of air pollution with daily GP consultations for asthma and other lower respiratory conditions in London, Thorax, 54(7), 597-605.
  16. [16]  McCracken, J.P., Albalak, R., Boy, E., Bruce, N., Hessen, J., Schei, M.A., and Smith, K.R. (1999), Improved Stove or Interfuel Substitution for Decreasing Indoor Air Pollution from Cooking with Biomass Fuels in Highland Guatemala, Indoor Air, 3, 118-23.
  17. [17]  Bj\"{o}rkst\{e}n, B. (1999), The environmental influence on childhood asthma, Allergy, 54, 17-23.
  18. [18]  Carvalho Coelho, A.C., Cardoso, B., Souza, L., Souza-Machado, C.D., and Souza-Machado, A. (2016), The impacts of educational asthma interventions in schools: a systematic review of the literature, Canadian respiratory journal, $2016$.
  19. [19]  Ionescu, C.M. and Copot, D. (2017), Monitoring respiratory impedance by wearable sensor device: Protocol and methodology, Biomedical Signal Processing and Control, 36, 57-62.-11
  20. [20]  Bates, J.H. (2009), Lung mechanics: an inverse modeling approach. Cambridge University Press.
  21. [21]  Ionescu, C., Desager, K., and De Keyser, R. (2011), Fractional order model parameters for the respiratory input impedance in healthy and in asthmatic children, Computer methods and programs in biomedicine, 101(3), 315-323.[I]
  22. [22]  Ionescu, C., Oustaloup, A., Levron, F., Melchior, P., Sabatier, J., and De Keyser, R. (2009), A model of the lungs based on fractal geometrical and structural properties, IFAC Proceedings Volumes, 42(10), 994-999.-2
  23. [23]  Ionescu, C. and De Keyser, R. (2008), Parametric models for characterizing respiratory input impedance, Journal of medical engineering {$\&$ technology}, 32(4), 315-324.-3
  24. [24]  Ionescu, C.M. and De Keyser, R. (2008), Relations between fractional-order model parameters and lung pathology in chronic obstructive pulmonary disease, IEEE Transactions on Biomedical Engineering, 56(4), 978-987-6
  25. [25]  Ionescu, C.M., Copot, D., and De Keyser, R. (2013), Respiratory impedance model with lumped fractional order diffusion compartment, IFAC Proceedings Volumes, 46(1), 260-265.-7
  26. [26]  Ionescu, C., Lopes, A., Copot, D., Machado, J.T., and Bates, J.H.T. (2017), The role of fractional calculus in modeling biological phenomena: A review. Communications in Nonlinear Science and Numerical Simulation, 51, 141-159.-5
  27. [27]  Ionescu, C., Machado, J.T., and De Keyser, R. (2011), Fractional-order impulse response of the respiratory system, Computers {$\&$ Mathematics with Applications}, 62(3), 845-854.-4.
  28. [28]  Faria, A.C., Veiga, J., Lopes, A.J., and Melo, P.L. (2016), Forced oscillation, integer and fractional-order modeling in asthma, Computer methods and programs in biomedicine, 128, 12-26.-8
  29. [29]  Ionescu, C.M. (2013), The human respiratory system: an analysis of the interplay between anatomy, structure, breathing and fractal dynamics, Springer Science & Business Media.-12
  30. [30]  Tawhai, M.H. and Bates, J.H. (2011), Multi-scale lung modeling, Journal of Applied Physiology, 110(5), 1466-1472.-9
  31. [31]  Ghosh, M. (2000), Industrial pollution and Asthma: A mathematical model, Journal of Biological Systems, 8(04), 347-371.
  32. [32]  RAM, N. and Tripathi, A. (2009), A Nonlinear Mathematical model for Asthma: Effect of Environmental Pollution, Iranian Journal of Optimization, 1(1), 24-56.
  33. [33]  Alejo, A.B. and Quesada, D.G. (2016), Modeling the association between the seasonal asthma prevalence and upper respiratory infections.
  34. [34]  Kim, Y., Lee, S., Kim, Y.S., Lawler, S., Gho, Y.S., Kim, Y.K., and Hwang, H.J. (2013), Regulation of Th1/Th2 cells in asthma development: a mathematical model. Mathematical Biosciences {$\&$ Engineering}, 10(4), 1095-1133.
  35. [35]  Tob\{\i}as, A., Campbell, M.J., and S\{a}ez, M. (1999), Modelling asthma epidemics on the relationship between air pollution and asthma emergency visits in Barcelona, Spain, European journal of epidemiology, 15(9), 799-803.
  36. [36]  Diekmann, O., Heesterbeek, J.A.P., and Metz, J.A. (1990), On the definition and the computation of the basic reproduction ratio R$_{0}$ in models for infectious diseases in heterogeneous populations, Journal of mathematical biology, 28(4), 365-382.
  37. [37]  Arino, J., McCluskey, C.C., and van den Driessche, P. (2003), Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM Journal on Applied Mathematics, 64(1), 260-276.
  38. [38]  McCluskey, C.C. and van den Driessche, P. (2004), Global analysis of two tuberculosis models, Journal of Dynamics and Differential Equations, 16(1), 139-166.
  39. [39]  Busenberg, S. and Van den Driessche, P. (1990), Analysis of a disease transmission model in a population with varying size, Journal of mathematical biology, 28(3), 257-270.
  40. [40]  Van den Driessche, P. and Watmough, J. (2002), Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180(1-2), 29-48.

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