Dynamical Model for Determining Human Susceptibility to Dengue Fever
- 1 Department of Mathematics, Faculty of Science and Technology, Suratthani Rajabhat University, Surat Thani, 84100, Thailand
- 2 Department of Physics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok, 10400, Thailand
Abstract
Problem statement: Mathematical models are a useful tool for understanding and describing the transmission of diseases such as dengue fever, one of the most prevalently emerging diseases common to tropical and subtropical areas throughout South East Asia. By taking into account human susceptibility to disease, the dynamics of a dengue disease model is proposed. Approach: Using standard methods for analyzing a system, the stability of the model is determined by using Routh-Hurwitz criteria. Results and Conclusion: We can show that the basic reproductive number (R0), the threshold parameter, when R0<1, the disease-free state is locally asymptotically stable. If R0>1, the endemic equilibrium state is locally asymptotically stable. Numerical results illustrate the dynamics of the disease within the context of varying parameter values.
DOI: https://doi.org/10.3844/ajassp.2011.1101.1106
Copyright: © 2011 Surapol Naowarat, Thanon Korkiatsakul and I. Ming Tang. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Dengue Shock Syndrome (DSS)
- Dengue Haemorrhagic Fever (DHF)
- Dengue fever (DF)
- Mathematical model
- female Aedes mosquitoes
- sequential infections