Mathematical Model for the Transmission of Two Plasmodium Malaria
Malaria is transmitted to the human by biting of
infected Anopheles mosquitoes. This disease is a serious, acute and
chronic relapsing infection to humans. Fever, nausea, vomiting, back
pain, increased sweating anemia and splenomegaly (enlargement of
the spleen) are the symptoms of the patients who infected with this
disease. It is caused by the multiplication of protozoa parasite of the
genus Plasmodium. Plasmodium falciparum, Plasmodium vivax,
Plasmodium malariae and Plasmodium ovale are the four types of
Plasmodium malaria. A mathematical model for the transmission of
Plasmodium Malaria is developed in which the human and vector
population are divided into two classes, the susceptible and the
infectious classes. In this paper, we formulate the dynamical model
of Plasmodium falciparum and Plasmodium vivax malaria. The
standard dynamical analysis is used for analyzing the behavior for
the transmission of this disease. The Threshold condition is found
and numerical results are shown to confirm the analytical results.
[1] WHO, "World malaria situation in 1994.(Weekly Epidemiology
Record)," , vol. 72, 1997, pp. 269-292.
[2] PCC.Garnhan, Malaria parasites of man: life- cycles and morphology
(excluding unltrastructure). IN W.H. Wernsdorfer and I. McGregor
(Eds).
[3] H.Mashaal, Clinical malariology. Southeast Asian Medical Information
Center, 1986.
[4] J.P. Kreier, Malaria volume1 epidemiology, chemotherapy,
morphology, and metabolism. New York : Academic press , 1980.
[5] G.MacDonald, The epidemiology and control of malaria. Oxford
University Press, London, 1957.
[6] R. Ross, The preventation of Malaria. 2th ed. Murray, London,1911.
[7] Division of Epidemiology, Annual Epidemiological Surveillance
Report, Ministry of Public Health Royal Thai Government, 1965-
2007.
[8] R.M.Anderson and R.M.May, Infectious Disease of Humans, Dynamics
and Control. Oxford U. Press, Oxford, 1991.
[9] A.Kammanee, N.Kanyamee and I.M.Tang, "Basic Reproduction
Number for the Transmission of Plasmodium Vivax Malaria,"
Southeast Asian J Trop Med and Pub Health , vol.32, pp.702-706,
2001.
[10] L.Esteva and C.Vargas, "Analysis of a dengue disease transmission
model," Math. BioSci, vol.150, pp.131-151, 1998.
[11] P.Pongsumpun and I.M.Tang, "The Transmission Model of P. falciparum
and P. Vivax Malaria between Thai and Burmese," International Journal
of Mathematical Models and Methods in Applied Sciences, vol. 3,
pp. 19-26, 2009.
[1] WHO, "World malaria situation in 1994.(Weekly Epidemiology
Record)," , vol. 72, 1997, pp. 269-292.
[2] PCC.Garnhan, Malaria parasites of man: life- cycles and morphology
(excluding unltrastructure). IN W.H. Wernsdorfer and I. McGregor
(Eds).
[3] H.Mashaal, Clinical malariology. Southeast Asian Medical Information
Center, 1986.
[4] J.P. Kreier, Malaria volume1 epidemiology, chemotherapy,
morphology, and metabolism. New York : Academic press , 1980.
[5] G.MacDonald, The epidemiology and control of malaria. Oxford
University Press, London, 1957.
[6] R. Ross, The preventation of Malaria. 2th ed. Murray, London,1911.
[7] Division of Epidemiology, Annual Epidemiological Surveillance
Report, Ministry of Public Health Royal Thai Government, 1965-
2007.
[8] R.M.Anderson and R.M.May, Infectious Disease of Humans, Dynamics
and Control. Oxford U. Press, Oxford, 1991.
[9] A.Kammanee, N.Kanyamee and I.M.Tang, "Basic Reproduction
Number for the Transmission of Plasmodium Vivax Malaria,"
Southeast Asian J Trop Med and Pub Health , vol.32, pp.702-706,
2001.
[10] L.Esteva and C.Vargas, "Analysis of a dengue disease transmission
model," Math. BioSci, vol.150, pp.131-151, 1998.
[11] P.Pongsumpun and I.M.Tang, "The Transmission Model of P. falciparum
and P. Vivax Malaria between Thai and Burmese," International Journal
of Mathematical Models and Methods in Applied Sciences, vol. 3,
pp. 19-26, 2009.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59562", author = "P. Pongsumpun", title = "Mathematical Model for the Transmission of Two Plasmodium Malaria", abstract = "Malaria is transmitted to the human by biting of
infected Anopheles mosquitoes. This disease is a serious, acute and
chronic relapsing infection to humans. Fever, nausea, vomiting, back
pain, increased sweating anemia and splenomegaly (enlargement of
the spleen) are the symptoms of the patients who infected with this
disease. It is caused by the multiplication of protozoa parasite of the
genus Plasmodium. Plasmodium falciparum, Plasmodium vivax,
Plasmodium malariae and Plasmodium ovale are the four types of
Plasmodium malaria. A mathematical model for the transmission of
Plasmodium Malaria is developed in which the human and vector
population are divided into two classes, the susceptible and the
infectious classes. In this paper, we formulate the dynamical model
of Plasmodium falciparum and Plasmodium vivax malaria. The
standard dynamical analysis is used for analyzing the behavior for
the transmission of this disease. The Threshold condition is found
and numerical results are shown to confirm the analytical results.", keywords = "Dynamical analysis, Malaria, mathematical model,threshold condition.", volume = "5", number = "3", pages = "446-5", }