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The Global Stability Using Lyapunov Function

Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084784

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References:


[1] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 1997.
[2] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 1998.
[3] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 1999.
[4] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2000.
[5] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2001.
[6] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2002.
[7] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2003.
[8] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2004.
[9] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2005.
[10] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2006.
[11] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2007.
[12] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2008.
[13] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2009.
[14] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2010.
[15] Division of Epidemiology, Annual Epidemiological Survillance Report, Ministry of Public Health, Thailand, 2011.
[16] Van der Hoeden, "Epizootiology of Leptospirosis," Adv. Vet. Med., vol. 4, pp. 277-339, 1958.
[17] R. L. Morter and E. V. Morse, "Experimental Leptospirosis II. The Role of Cales in the Transmission of Leptospira Pomona Among Cattle, Swine, Sheep and Goats," J. A. V. M. A., vol. 128, pp. 408-443, 1956.
[18] S. Faine, Guidelines for the control of Leptospirosis. Gevena: Wolrd Health Organization, 1982.
[19] C. Caporale, "Aspetti patogeneticie clinici delle leptospirosi dei ruminanti," Atti Primo Simposio Naz. Sulle Leptospirosi Pisa, pp. 13- 14, 1962.
[20] K. L . Fennestad, Experimental Leptospirosis in Calves, Munkgaard: Copenhagen, 1963.
[21] L. M. Ringen, F. K. Bracken, S. G. Kenzy and R. W. Gillespei, "Studies on bovine leptospirosis. I. Some effects of dihydrostreptomycin and Terramycin on the carrier condition in bovine leptospirosis," J. Amer. Vet. Med. Ass., vol. 126, pp. 272-276, 1955.
[22] M. Ristic, M. M. Galton, L. Mcrae, D. A. Sanders and J. H. Steele, "Experimental leptospirosis in bovinees. I. Establishment of Infection with Leptospirosis Sejroe," J. Infect. Dis., vol. 100, pp. 228-240, 1957.
[23] J. Yunibandhu, "First report of Weil-s disease in Thailand," J. Med. Assoc. Thai, vol. 26, pp. 83, 1943.
[24] Edelstein Keshet, Leah, Mathematical models inbiology, Random House of Canada, 1988.
[25] W. Triumpo, D. Baowan, I. M. Tang, N. Nuttavut, J. Wong-Ekkabut and G. Doungchawee, "A simple deterministic Model for the spread of Leptospirosis in Thailand," World Academy of Science, Engineering and Technology, vol. 13, pp. 170-174, 2006.
[26] J. Holt, S. Davis and H. Leirs, "A model of Leptospirosis infection infection in an African rodent to determine risk to human: Seasonal fluctuations and the impact of rodent control," Acta Tropica, vol. 99, pp. 218-225, 2006.
[27] P. Pongsumpun, T. Manmai and R. Kongnuy, "Age Structural Transmission Model for Leptospirosis," The 3rd International Symposium on Biomedical Engineering (ISBME 2008), pp. 411-416, 2008.
[28] R. Kongnuy and E. Naowanich, "Stability and Lyapunov Functions for the Dynamics of Leptospirosis," The 2011 Biomedical Engineering International Conference (BMEiCON 2011), pp. 17-21, 2011.
[29] J. D. Murray, Mathematical biology I. An Introduction. USA, 2002.
[30] F. Brauer, C. Castillo-Chavez, Mathematical models in population biology and epidemiology. Springer-Verlag, New York, 2001.
[31] H. W. Hethcote, "Mathematics of infectious diseases," SIAM Rev, vol. 42, pp. 599-653, 2000.
[32] J. P. LaSalle, The stability of dynamical systems, Philadelphia: SIAM, 1976.