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Mathematical Model of Leptospirosis: Linearized Solutions and Stability Analysis
Industrial Mathematics Research Unit and Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand；Center of Excellence in Mathematics, Bangkok, Thailand
Institute of Natural and Mathematical Sciences, College of Sciences, Massey University, Auckland, New Zealand
Center of Excellence in Mathematics, Bangkok, Thailand；R and D Group of Biological and Environment Physics (BIOPHYSICS), Department of Physics, Faculty of Science, Mahidol University, Bangkok, Thailand
Center of Excellence in Mathematics, Bangkok, Thailand；Institute of Natural and Mathematical Sciences, College of Sciences, Massey University, Auckland, New Zealand；Institute for Innovative Learning, Mahidol University, Nakorn Prathom, Thailand
Institute of Natural and Mathematical Sciences, College of Sciences, Massey University, Auckland, New Zealand
- 1 Industrial Mathematics Research Unit and Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand；Center of Excellence in Mathematics, Bangkok, Thailand
- 2 Institute of Natural and Mathematical Sciences, College of Sciences, Massey University, Auckland, New Zealand
- 3 Center of Excellence in Mathematics, Bangkok, Thailand；R and D Group of Biological and Environment Physics (BIOPHYSICS), Department of Physics, Faculty of Science, Mahidol University, Bangkok, Thailand
- 4 Center of Excellence in Mathematics, Bangkok, Thailand；Institute of Natural and Mathematical Sciences, College of Sciences, Massey University, Auckland, New Zealand；Institute for Innovative Learning, Mahidol University, Nakorn Prathom, Thailand
- 5 Institute of Natural and Mathematical Sciences, College of Sciences, Massey University, Auckland, New Zealand
Applied Mathematics·Volume 04 (2013)·Pages 77–84·Published 30 September 2013·DOI10.4236/am.2013.410A2008
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Abstract
In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used to study the stability analysis, analytical solution and global behavior of the spreading of the disease. The model was analysed using the techniques of non-linear dynamical systems. Two equilibrium points were found and the stability conditions for these equilibrium points were established. It will be shown that the linearised solutions of the sir equations are in good agreement with numerical solutions.
KeywordsTechnologyPreference for QualityVolume of TradeVertical Intra-Industry Trade
- W. Triampo, et al., “A Simple Deterministic Model for the Spread of Leptospirosis in Thailand,” International Journal of Biological and Medical Sciences, Vol. 2, No. 1, 2007, p. 22.
- V. Michel, C. Branger and G. Andre-Fontaine, “Epidemiology of Leptospirosis,” Revista Cubana de Medicina Tropical, Vol. 54, No. 1, 2002, pp. 7-10.
- J. D. Murray, “Mathematical Biology,” 2nd Edition, SpringerVerlag, Berlin, 2004. http://dx.doi.org/10.1007/b98868
- P. K. Tapaswi and J. Chattopadhyay, “Global Stability Results of a Susceptible-Infective-Immune-Susceptible (SIRS) Epidemic Model,” Ecological Modelling, Vol. 87, No. 1-3, 1996, pp. 223-226.
- L. Cai and X.-Z. Li, “Global Analysis of a Vector-Host Epidemic Model with Nonlinear Incidences,” Applied Mathematics and Computation, Vol. 217, No. 7, 2010, pp. 3531-3541.
- J. Holt, S. Davis and H. Leirs, “A Model of Leptospirosis Infection in an African Rodent to Determine Risk to Human: Seasonal Fluctuations and the Impact of Rodent Control,” Acta Tropica, Vol. 99, No. 2-3, 2006, pp. 218225.
- S. M. O’Regan, T. C. Kelly, A. Korobeinikov, M. J. A. O’Callaghan and A. V. Pokrovskii, “Lyapunov Functions for Sir and Sirs Epidemic Models,” Applied Mathematics Letters, Vol. 23, No. 4, 2010, pp. 446-448.