# Statistics Based Models for the Dynamics of Chernivtsi Children Disease

## Authors

• Igor G. Nesteruk Institute of Hydromechanics, National Academy of Sciences of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Ukraine

## Keywords:

Model identification, Parameter identification, Statistical methods, Mathematical modeling of infection diseases, SIR-model, Contamination models

## Abstract

Background. Simple mathematical models of contamination and SIR-model of spreading an infection were used to simulate the time dynamics of the unknown before children disease, which occurred in Chernivtsi (Ukraine). The cause of many cases of alopecia, which began in this city in August 1988 is still not fully clarified. According to the official report of the governmental commission, the last new cases occurred in the middle of November 1988, and the reason of the illness was reported as chemical exogenous intoxication. Later this illness became the name “Chernivtsi chemical disease”. Nevertheless, the significantly increased number of new cases of the local alopecia was registered almost three years and is still not clarified.

Objective. The comparison of two different versions of the disease: chemical exogenous intoxication and infection. Identification of the parameters of mathematical models and prediction of the disease development.

Methods. Analytical solutions of the contamination models and SIR-model for an epidemic are obtained. The optimal values of parameters with the use of linear regression were found.

Results. The optimal values of the models parameters with the use of statistical approach were identified. The calculations showed that the infectious version of the disease is more reliable in comparison with the popular contamination one. The possible date of the epidemic beginning was estimated.

Conclusions. The optimal parameters of SIR-model allow calculating the realistic number of victims and other characteristics of possible epidemic. They also show that increased number of cases of local alopecia could be a part of the same epidemic as “Chernivtsi chemical disease”.

## References

D.D. Zerbino et al., “The results of a study of chemical-induced disease in children in Chernovtsy”, Vrach. Delo, vol. 8, pp. 88–91, 1991 (in Russian).

D.D. Zerbino and A.M. Serdiuk, Chernivtsi Chemical Disease, New Ecologic Pathology? (Essays about epidemiology, clinic revealings, etiology, versions of genesis, documents). Lviv, Ukraine: Missioner, 1998 (in Ukrainian).

V.K. Patratii et al., “Chemical intoxication syndrome in children with diffuse alopecia”, Pediatriia, no. 12, pp. 52–55, 1991 (in Russian).

V.K. Tatochenko et al., “An epidemic outbreak of diffuse alopecia in children”, Pediatriia, no. 12, pp. 67–71, 1990 (in Russian).

N.R. Draper and H. Smith, Applied Regression Analysis, 3rd ed. New York: John Wiley, 1998.

Structured-Population Models in Marine, Terrestrial, and Fresh-Water Systems, S. Tuljapurkar and H. Caswell, eds. Springer, 1997.

The Radiological Accident in Goiania. Vienna, Austria: International Atomic Energy Agency, 1988.

W.D. Kermack and A.G. McKendrick, “A contribution to the mathematical theory of epidemics”, J. Royal Statistical Society, Ser. A, vol. 115, pp. 700–721, 1927.

J.D. Murray, Mathematical Biology I/II. New York: Springer, 2002.

N.T.J. Bailey, The Mathematical Theory of Epidemics. London, UK: Griffin Book Co., 1957.

D. Langemann et al., “Comparison of mathematical models for the dynamics of the Chernivtsi children disease”, Mathematics in Computers and Simulation, vol. 123, pp. 68–79, 2016. doi: 10.1016/j.matcom.2016.01.003

W. Pschyrembel, Klinisches Woerterbuch. Berlin, Germany: de Gruyter, 2013.

Chantal Bolduc (2017, May 08). Alopecia Areata [Online]. Available: http://emedicine.medscape.com/article/1069931-overview

P. Waltman, Deterministic Threshold Models in the Theory of Epidemics, in Lecture Notes in Biomathematics, vol. 1. Springer, 1974.