Mathematical Modeling for Dengue Transmission with the Effect of Season
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:49359", author = "R. Kongnuy. and P. Pongsumpun", title = "Mathematical Modeling for Dengue Transmission with the Effect of Season", 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.", volume = "5", number = "3", pages = "212-5", }