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
Cite this paper
B. Pimpunchat, G. Wake, C. Modchang, W. Triampo and A. Babylon, "Mathematical Model of Leptospirosis: Linearized Solutions and Stability Analysis," Applied Mathematics
, Vol. 4 No. 10, 2013, pp. 77-84. doi: 10.4236/am.2013.410A2008
 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.
 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.