Prediction of the Effects of Combustion–Generated Pollutant on Human Health: Mathematical Models and Numerical Solutions


Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria


The rapid increase in technological innovations and utilizations have adversely affected the environment and consequently continued to constitute a threat to the future survival of human. To counter these assaults and the threats of further degradation of the environment and human health, the basic recommended approach for predicting the impact of the pollution and for the determination of the risk assessment strategies is through the use of mathematical models. Therefore, this work presents mathematical models for the prediction of the effects of combustion generated pollutants, such as Carbon-monoxide (CO) on human health. The developed coupled system of nonlinear partial differential equation for the ambient concentration of carbon mono-oxide in which the human subject was exposed to and the concentration of Carboxyhemoglobin (COHb) in the blood is solved numerically using Alternating-Direct Implicit (ADI) scheme. From the computations, the variables of the models show significant results in their variations and the standard error of the predicted results from the model range in between 0.5-0.85 for the different concentrations of ambient carbon monoxide. This established that the computed results show good agreement with available experimental data. Therefore, the model can be used as a means of controlling the effects of the pollutant on human health and the results will serve as a way of evaluating our technological injuries, effectively controlling our pollutants emissions and also as a tool for designing and developing better equipments and engines with lower carbon or pollutants emissions.


1.     Act, C.A., 1967. as amended (42 USC 1857 l857L) Sec 107. Sec lll. November, 21.

2.     El Harbawi, M., S. Mustapha, T.S.Y. Choong, S.A. Rashid, S. Kadir and Z.A. Rashid, 2008. Rapid analysis of risk assessment using developed simulation of chemical industrial accidents software package. International Journal of Environmental Science & Technology, 5(1): 53-64.

3.     Singh, M., M. Sharan and S. Selvakumar, 1991. A mathematical model for the computation of carboxyhaemoglobin in human blood as a function of exposure time. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 334(1269): 135-147.

4.     Gallagher, F. and H. Mason, 2004. Carbon monoxide poisoning in two workers using an LPG forklift truck within a coldstore. Occupational medicine, 54(7): 483-488.

5.     Ren, C. and S. Tong, 2008. Health effects of ambient air pollution–recent research development and contemporary methodological challenges. Environmental Health, 7(1): 56.

6.     Forbes, W., F. Sargent and F. Roughton, 1945. The rate of carbon monoxide uptake by normal men. American Journal of Physiology--Legacy Content, 143(4): 594-608.

7.     Forster, R., W. Fowler and D. Bates, 1954. Considerations on the uptake of carbon monoxide by the lungs. Journal of Clinical Investigation, 33(8): 1128.

8.     Peterson, J.E. and R.D. Stewart, 1975. Predicting the carboxyhemoglobin levels resulting from carbon monoxide exposures. Journal of Applied Physiology, 39(4): 633-638.

9.     BERNARD, T.E. and J. DUKER, 1981. Modeling carbon monoxide uptake during work. The American Industrial Hygiene Association Journal, 42(5): 361-364.

10.   I., T., U. Y., I. K. and k. H., 1981. Prediction of the carbonmonoxyhemoglobin levels during and after carbon monoxide exposures in various animal species. The Japanese journal of physiology, 31(2): 131-143.

11.   Collier, C.R. and J.R. Goldsmith, 1983. Interactions of carbon monoxide and hemoglobin at high altitude. Atmospheric Environment (1967), 17(4): 723-728.

12.   Roughton, F. and R. Darling, 1944. The effect of carbon monoxide on the oxyhemoglobin dissociation curve. American Journal of Physiology--Legacy Content, 141(1): 17-31.

13.   Weir, F. and D.C. Viano, 1977. Prediction of carboxyhemoglobin concentration from transient carbon monoxide exposure. Aviation, space, and environmental medicine, 48(11): 1076-1080.

14.   Marcus, A.H., 1980. Mathematical models for carboxyhemoglobin. Atmospheric Environment (1967), 14(7): 841-844.

15.   Tikuisis, P., H. Madill, B. Gill, W. Lewis, K. Cox and D. Kane, 1987. A critical analysis of the use of the CFK equation in predicting COHb formation. The American Industrial Hygiene Association Journal, 48(3): 208-213.

16.   Wallace, L., J. Thomas, D. Mage and W. Ott, 1988. Comparison of breath CO, CO exposure, and Coburn model predictions in the US EPA Washington-Denver (CO) study. Atmospheric Environment (1967), 22(10): 2183-2193.

17.   Ott, W.R. and D.T. Mage, 1978. Interpreting urban carbon monoxide concentrations by means of a computerized blood COHb model. Journal of the Air Pollution Control Association, 28(9): 911-916.

18.   Venkatram, A. and R. Louch, 1979. Evaluation of CO air quality criteria using a COHb model. Atmospheric Environment (1967), 13(6): 869-872.

19.   Nevers, N.d., Air Pollution control Engineering2000, New York: McGraw Hill.

20.   Coburn, R.F. and H.J. Forman, 1987. Carbon monoxide toxicity. Handbook of physiology, section, 3: 439-456.

21.   Osgood, E.E., 1955. Development and growth of hematopoietic tissues with a clinically practical method of growth analysis. Pediatrics, 15(6): 733-751.

22.   Gibson, Q. and F. Roughton, 1955. The kinetics of dissociation of the first oxygen molecule from fully saturated oxyhaemoglobin in sheep blood solutions. Proceedings of the Royal Society of London B: Biological Sciences, 143(912): 310-334.

23.   Murray, J. and J. Wyman, 1971. Facilitated Diffusion THE CASE OF CARBON MONOXIDE. Journal of Biological Chemistry, 246(19): 5903-5906.

24.   Holland, R.A., 1970. Reaction rates of carbon monoxide and hemoglobin*. Annals of the New York Academy of Sciences, 174(1): 154-171.

25.   Guyton, A.C., Textbook of medical physiology1981: W. B. Saunders.

26.   Thew, G.a.V., P., Automatic functions in human physiology1985: Springer-Verlag.