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Mathematical Modeling for Dengue Transmission with the Effect of Season

Authors: R. Kongnuy., P. Pongsumpun

Abstract:

Mathematical models can be used to describe the transmission of disease. Dengue disease is the most significant mosquito-borne viral disease of human. It now a leading cause of childhood deaths and hospitalizations in many countries. Variations in environmental conditions, especially seasonal climatic parameters, effect to the transmission of dengue viruses the dengue viruses and their principal mosquito vector, Aedes aegypti. A transmission model for dengue disease is discussed in this paper. We assume that the human and vector populations are constant. We showed that the local stability is completely determined by the threshold parameter, 0 B . If 0 B is less than one, the disease free equilibrium state is stable. If 0 B is more than one, a unique endemic equilibrium state exists and is stable. The numerical results are shown for the different values of the transmission probability from vector to human populations.

Keywords: Dengue disease, mathematical model, season, threshold parameters.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327917

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References:


[1] World Health Organization, Dengue Haemorrhagic Fever: Diagnosis, Treatment, Prevention and Control. Geneva, 1997.
[2] D. J. Gubler, Dengue, CRC: Boca Raton, 1986, pp. 213.
[3] Division of Epidemiology, Annual Epidemiological Surveillance Report, Ministry of Public Health Royal Thai Government, 1999-2008.
[4] D. Bernoulli, "Essai d-une nonvelle analyse de la mortalite causee par la petite verole, et des advantages de l-inocubation pour la preventer," Acad. R. Sci, pp. 1-95, 1760.
[5] L. Esteva, and C. Vargas, "Analysis of a dengue disease transmission model," Math. BioSci, vol. 150, pp. 131-151, 1998.
[6] M. Robert, Stability and Complexity in Model Ecosystems. Princeton University Press, New Jersey, 1997.
[7] R. M. Anderson, and R. M. May, Infectious Diseases of Humans, Dynamics and control. Oxford U. Press, Oxford, 1991.