Mathematical Model of Leptospirosis: Linearized Solutions and Stability Analysis

B. Pimpunchat, G. C. Wake, C. Modchang, W. Triampo, A. M Babylon

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.
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.
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.

DOI: 10.4236/am.2013.410A2008                

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.

Keywords

Technology; Preference for Quality; Volume of Trade; Vertical Intra-Industry Trade

Conflicts of Interest

The authors declare no conflicts of interest.

References

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