Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans
Leptospirosis occurs worldwide (except the
poles of the earth), urban and rural areas, developed and
developing countries, especially in Thailand. It can be
transmitted to the human by rats through direct and indirect
ways. Human can be infected by either touching the infected rats
or contacting with water, soil containing urine from the infected
rats through skin, eyes and nose. The data of the people who
are infected with this disease indicates that most of the
patients are adults. The transmission of this disease is studied
through mathematical model. The population is separated into human
and rat. The human is divided into two classes, namely juvenile
and adult. The model equation is constructed for each class. The
standard dynamical modeling method is then used for
analyzing the behaviours of solutions. In addition, the
conditions of the parameters for the disease free and endemic
states are obtained. Numerical solutions are shown to support the
theoretical predictions. The results of this study guide the way to
decrease the disease outbreak.
[1] A.R. Bharti, J.E.Nally, J.N.Ricaldi, M.A.Matthias, M.M.Diaz,
M.A.Lovett, P.N.Levett, R.H.Gilman, M.R.Willig, E.Gotuzzo, and J.M.
"Leptospirosis: a zoonotic disease of global importance", Lancet
Infectious Diseases, vol.12, pp.757-771, 2003.
[2] W.Tangkanakul, H.L.Smits, S.Jatanasen, and D.A.Ashford,
"Leptospirosis: an emerging health problem in Thailand", Southeast
Asian Journal of Tropical Medicine and Public Health, vol.36,no.2,
pp.281-288, 2005.
[3] R. Inada , Y. Ido , and et al, "Etiology mode of infection and specific
therapy of Weil's disease", The Journal of Experimental medicine,vol.
23, pp.377-402, 1916.
[4] R. C. Abdulkader , A. C. Seguro , P. S. Malheiro, and et al, "Peculiar
electrolytic and hormonal abnormalities in acute renal failure due to
leptospirosis", The American Journal of Tropical Medicine and
Hygiene, vol. 51, no. 1, pp. 1-6, 1996.
[5] V. M. Arean , G. Sarasin, and J. H. Green, "The pathogenesis of
leptospirosis: toxin production by leptospira icterohaemorrha -giae",
American Journal of Veterinary Research, vol. 28, pp. 836-43, 1964.
[6] V. M. Arean , "Studies on the pathogenesis of leptospirosis.II, A
clinicopathologic evaluation of hepatic and renal function in
experimental leptospira infections", Laboratory Investigation, vol. 11,
pp.273-88, 1962.
[7] S. Barkay , and H. Garzozi , "Leptospirosis and uveitis," Annals of
Ophthalmology, vol. 16, no. 2, pp. 164-8, 1984.
[8] S. Faine, "Guideline for control of leptospirosis", World Health
Organization Geneva, vol. 67, pp.129, 1982
[9] J.Holt, S.Davis and H.Leirs, "A model of Leptospirosis infection in
African rodent to determine risk to humans : Seasonal fluctuations and
the impact of rodent control", Acta Tropica, vol. 99, pp. 218 - 225,
2006.
[10] W. Triampo, D. Baowan, I. M. Tang, N. Nuttavut, J. Wong- Ekkabut
and G. Doungchawee, "A Simple Deterministic Model for the Spread of
Leptospirosis in Thailand," International Journal of Biomedical
Sciences, vol 2, pp. 1306 -1216, 2007.
[11] R. M. Anderson and R.M. May, Infectious Diseases of Humans:
Dynamics and Control, Oxford University Press, Oxford, 1991.
[12] Division of Epidemiology, Annual Epidemiological Surveillance Report,
Ministry of Public Health, Royal Thai Government, 2002-2010.
[13] Edelstein - Keshet, Leah, Mathematical models in biology, Random
House of Canada, 1988.
[14] P.Pongsumpun, and I. M . Tang, "Mathematical model for the
transmission of Plasmodium Vivax Malaria," International Journal of
mathematical models and methods in applied sciences, vol. 3, pp.117-
121, 2007.
[15] P.Pongsumpun, and I. M . Tang, "Limit Cycle and Chaotic Behaviors
for the Transmission Model of Plasmodium Vivax Malaria
,"International Journal of mathematical models and methods in applied
sciences, vol.2, pp.563-570, 2008.
[1] A.R. Bharti, J.E.Nally, J.N.Ricaldi, M.A.Matthias, M.M.Diaz,
M.A.Lovett, P.N.Levett, R.H.Gilman, M.R.Willig, E.Gotuzzo, and J.M.
"Leptospirosis: a zoonotic disease of global importance", Lancet
Infectious Diseases, vol.12, pp.757-771, 2003.
[2] W.Tangkanakul, H.L.Smits, S.Jatanasen, and D.A.Ashford,
"Leptospirosis: an emerging health problem in Thailand", Southeast
Asian Journal of Tropical Medicine and Public Health, vol.36,no.2,
pp.281-288, 2005.
[3] R. Inada , Y. Ido , and et al, "Etiology mode of infection and specific
therapy of Weil's disease", The Journal of Experimental medicine,vol.
23, pp.377-402, 1916.
[4] R. C. Abdulkader , A. C. Seguro , P. S. Malheiro, and et al, "Peculiar
electrolytic and hormonal abnormalities in acute renal failure due to
leptospirosis", The American Journal of Tropical Medicine and
Hygiene, vol. 51, no. 1, pp. 1-6, 1996.
[5] V. M. Arean , G. Sarasin, and J. H. Green, "The pathogenesis of
leptospirosis: toxin production by leptospira icterohaemorrha -giae",
American Journal of Veterinary Research, vol. 28, pp. 836-43, 1964.
[6] V. M. Arean , "Studies on the pathogenesis of leptospirosis.II, A
clinicopathologic evaluation of hepatic and renal function in
experimental leptospira infections", Laboratory Investigation, vol. 11,
pp.273-88, 1962.
[7] S. Barkay , and H. Garzozi , "Leptospirosis and uveitis," Annals of
Ophthalmology, vol. 16, no. 2, pp. 164-8, 1984.
[8] S. Faine, "Guideline for control of leptospirosis", World Health
Organization Geneva, vol. 67, pp.129, 1982
[9] J.Holt, S.Davis and H.Leirs, "A model of Leptospirosis infection in
African rodent to determine risk to humans : Seasonal fluctuations and
the impact of rodent control", Acta Tropica, vol. 99, pp. 218 - 225,
2006.
[10] W. Triampo, D. Baowan, I. M. Tang, N. Nuttavut, J. Wong- Ekkabut
and G. Doungchawee, "A Simple Deterministic Model for the Spread of
Leptospirosis in Thailand," International Journal of Biomedical
Sciences, vol 2, pp. 1306 -1216, 2007.
[11] R. M. Anderson and R.M. May, Infectious Diseases of Humans:
Dynamics and Control, Oxford University Press, Oxford, 1991.
[12] Division of Epidemiology, Annual Epidemiological Surveillance Report,
Ministry of Public Health, Royal Thai Government, 2002-2010.
[13] Edelstein - Keshet, Leah, Mathematical models in biology, Random
House of Canada, 1988.
[14] P.Pongsumpun, and I. M . Tang, "Mathematical model for the
transmission of Plasmodium Vivax Malaria," International Journal of
mathematical models and methods in applied sciences, vol. 3, pp.117-
121, 2007.
[15] P.Pongsumpun, and I. M . Tang, "Limit Cycle and Chaotic Behaviors
for the Transmission Model of Plasmodium Vivax Malaria
,"International Journal of mathematical models and methods in applied
sciences, vol.2, pp.563-570, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57764", author = "P. Pongsumpun", title = "Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans", abstract = "Leptospirosis occurs worldwide (except the
poles of the earth), urban and rural areas, developed and
developing countries, especially in Thailand. It can be
transmitted to the human by rats through direct and indirect
ways. Human can be infected by either touching the infected rats
or contacting with water, soil containing urine from the infected
rats through skin, eyes and nose. The data of the people who
are infected with this disease indicates that most of the
patients are adults. The transmission of this disease is studied
through mathematical model. The population is separated into human
and rat. The human is divided into two classes, namely juvenile
and adult. The model equation is constructed for each class. The
standard dynamical modeling method is then used for
analyzing the behaviours of solutions. In addition, the
conditions of the parameters for the disease free and endemic
states are obtained. Numerical solutions are shown to support the
theoretical predictions. The results of this study guide the way to
decrease the disease outbreak.", keywords = "Adult human, juvenile human, leptospirosis, mathematical model.", volume = "6", number = "12", pages = "1699-6", }