Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans

Authors: P. Pongsumpun

Abstract:

Leptospirosis occurs worldwide (except the poles of the earth), urban and rural areas, developed and developing countries, especially in Thailand. It can be transmitted to the human by rats through direct and indirect ways. Human can be infected by either touching the infected rats or contacting with water, soil containing urine from the infected rats through skin, eyes and nose. The data of the people who are infected with this disease indicates that most of the patients are adults. The transmission of this disease is studied through mathematical model. The population is separated into human and rat. The human is divided into two classes, namely juvenile and adult. The model equation is constructed for each class. The standard dynamical modeling method is then used for analyzing the behaviours of solutions. In addition, the conditions of the parameters for the disease free and endemic states are obtained. Numerical solutions are shown to support the theoretical predictions. The results of this study guide the way to decrease the disease outbreak.

Keywords: Adult human, juvenile human, leptospirosis, mathematical model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071362

References:

[1] A.R. Bharti, J.E.Nally, J.N.Ricaldi, M.A.Matthias, M.M.Diaz, M.A.Lovett, P.N.Levett, R.H.Gilman, M.R.Willig, E.Gotuzzo, and J.M. "Leptospirosis: a zoonotic disease of global importance", Lancet Infectious Diseases, vol.12, pp.757-771, 2003.
[2] W.Tangkanakul, H.L.Smits, S.Jatanasen, and D.A.Ashford, "Leptospirosis: an emerging health problem in Thailand", Southeast Asian Journal of Tropical Medicine and Public Health, vol.36,no.2, pp.281-288, 2005.
[3] R. Inada , Y. Ido , and et al, "Etiology mode of infection and specific therapy of Weil's disease", The Journal of Experimental medicine,vol. 23, pp.377-402, 1916.
[4] R. C. Abdulkader , A. C. Seguro , P. S. Malheiro, and et al, "Peculiar electrolytic and hormonal abnormalities in acute renal failure due to leptospirosis", The American Journal of Tropical Medicine and Hygiene, vol. 51, no. 1, pp. 1-6, 1996.
[5] V. M. Arean , G. Sarasin, and J. H. Green, "The pathogenesis of leptospirosis: toxin production by leptospira icterohaemorrha -giae", American Journal of Veterinary Research, vol. 28, pp. 836-43, 1964.
[6] V. M. Arean , "Studies on the pathogenesis of leptospirosis.II, A clinicopathologic evaluation of hepatic and renal function in experimental leptospira infections", Laboratory Investigation, vol. 11, pp.273-88, 1962.
[7] S. Barkay , and H. Garzozi , "Leptospirosis and uveitis," Annals of Ophthalmology, vol. 16, no. 2, pp. 164-8, 1984.
[8] S. Faine, "Guideline for control of leptospirosis", World Health Organization Geneva, vol. 67, pp.129, 1982
[9] J.Holt, S.Davis and H.Leirs, "A model of Leptospirosis infection in African rodent to determine risk to humans : Seasonal fluctuations and the impact of rodent control", Acta Tropica, vol. 99, pp. 218 - 225, 2006.
[10] W. Triampo, D. Baowan, I. M. Tang, N. Nuttavut, J. Wong- Ekkabut and G. Doungchawee, "A Simple Deterministic Model for the Spread of Leptospirosis in Thailand," International Journal of Biomedical Sciences, vol 2, pp. 1306 -1216, 2007.
[11] R. M. Anderson and R.M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
[12] Division of Epidemiology, Annual Epidemiological Surveillance Report, Ministry of Public Health, Royal Thai Government, 2002-2010.
[13] Edelstein - Keshet, Leah, Mathematical models in biology, Random House of Canada, 1988.
[14] P.Pongsumpun, and I. M . Tang, "Mathematical model for the transmission of Plasmodium Vivax Malaria," International Journal of mathematical models and methods in applied sciences, vol. 3, pp.117- 121, 2007.
[15] P.Pongsumpun, and I. M . Tang, "Limit Cycle and Chaotic Behaviors for the Transmission Model of Plasmodium Vivax Malaria ,"International Journal of mathematical models and methods in applied sciences, vol.2, pp.563-570, 2008.