Effect of the Seasonal Variation in the Extrinsic Incubation Period on the Long Term Behavior of the Dengue Hemorrhagic Fever Epidemic
The incidences of dengue hemorrhagic disease (DHF)
over the long term exhibit a seasonal behavior. It has been
hypothesized that these behaviors are due to the seasonal climate
changes which in turn induce a seasonal variation in the incubation
period of the virus while it is developing the mosquito. The standard
dynamic analysis is applied for analysis the Susceptible-Exposed-
Infectious-Recovered (SEIR) model which includes an annual
variation in the length of the extrinsic incubation period (EIP). The
presence of both asymptomatic and symptomatic infections is
allowed in the present model. We found that dynamic behavior of the
endemic state changes as the influence of the seasonal variation of
the EIP becomes stronger. As the influence is further increased, the
trajectory exhibits sustained oscillations when it leaves the chaotic
region.
[1] S.F. Dowell, "Seasonal Variation in Host Susceptibility
and Cycles of Certain Infectious Disease", Emerg. Infect.Dis.,
vol.7, no.3, 2002, pp.369-373.
[2] J.Brownlee, "An investigation into the periodicity of measles
epidemics in London from 1703 to the present day by the method
of the periodiogram.", Phil. Trans. Roy. Soc.London B, vol.208,
1918, pp. 225-250.
[3] R.J. Nelson ,and D.L.Drasen, "Melatonin mediates seasonal
adjustments in immune function", Res.Nutr.Dev., vol.39, no.3,
1999, pp.383-398.
[4] S.F.Dowell, C.G.Whitney, C.Wright, C.E.Rose, and
Jr,Schuchat, "Seasonal patterns of invasive pneumococcal disease",
Emerg. Infect. Dis., vol. 9, no.5, 2003, pp. 573-579.
[5] G.Blanc, and J.Caminopetroa, "Researches experiments surla dengue",
Ann. Inst. Pasteur., vol.44, 1930, pp.367- 436.
[6] S.Hales, P.Weinstein, and A.Woodward, "Dengue Fever Epidemic
in the South Pacific driven by El Nino Southern Oscillation", Lancet ,
vol. 348, 1996, pp.1664-1665.
[7] R.Anderson, B.T.Greenfell , and R.M.May, " Oscillatory fluctuations
in the incidence of infectious disease and the impact of vaccination:
time series analysis", J.Hyg.Camb, vol.93, 1984, pp. 587-608.
[8] N.M.Ferguson, D.J.Nokes, R.M.Anderson, "Dynamical complexity in
age-structure models of transmission of the measles virus:
Epidemiological implications at highlevels of vaccine uptake", Math.
Biosci. , vol..138, 1996., pp.101-130.
[9] D.M.Watts, D.S.Burke, B.A.Harrison, R.E.Whitmire, and A. Nisalak,
"Effect of temperature on the vector Efficiency of Aedes aegypti for
dengue 2 virus ", Am.J.Trop.Med.Hyg., vol.36, 1987, pp. 143-152.
[10] WHO, Dengue hemorrhagic fever, diagnosis, treatment and control.
World Health Organization, Geneva, Switzerland, 1986.
[11] D.J.Gubler, "Dengue hemorrhagic Fever", Clin.Microbiol.Rev.,
vol.11, 1998, pp. 480-491.
[12] D.S.Burke, A.Nisalak, D.Johnson, and R.M.Scott, " A prospective
study of dengue infections in Bangkok", Am. J.Trop. Med. Hyg., vol.
38, 1988, pp.172-180.
[13] G.Kuri , P..Mas, M.Soler, A.Goyenechea, and L.Morier, "Dengue
hemorrhagic fever in Cuba, 1981: rapid Diagnosis of the etiologic
agent", Bull. Pan. Am. Health. Org., vol.17, 1983, pp.126-132.
[14] J.E.Marsden, and M.McCraken, The Hopf bifurcation and its
application. Springer-Verlag(New York), 1976.
[15] D.W.Vanghn, S.Green, S.Kalayanarooj, B.L.Innis, S.Nimmannitya,
A.Santayakorn, and et al, "Dengue in the early febrile phase, viremia
and antibody responses", J.Inf.Dis., vol.176, 1997, pp..322-330.
[16] S.Gupta, J.Swinton, and R.M.Anderson, "Theoretical studies of
the effects of heterogeneity in the parasite population on the
transmission dynamics of malaria", Proc.Roy.Soc.London B, vol.256,
1994, pp. 231-238.
[17] M.Yasuno, and R.J.Tonn, "A study of the biting habits of Aedes
aegypti in Bangkok", Bull World Health Organ. vol.43, 1970,
319-325.
[18] L.F.Olsen ,G.L.Trusty, and W.M.Schaffer, "Oscillation and Chaos in
epidemics: a nonlinear dynamics study of six childhood diseases in
Copenhagen, Denmark", Theor. Populat. Biol., vol.33, 1988, pp. 344-
370.
[19] S.Gakkhar, and R.K.Naji , "Chaos in seasonally perturbed ratiodependent
prey-predator system", Chaos, Solitons & Fractals, vol.18,
2003, pp.107-118.
[20] S.Gakkhar, and R.K.Naji, "Seasonally perturbed prey-predator system
with predator-dependent functional response ", Chaos, Solitons &
fractals, vol.18, 2003, pp. 1075-1083.
[1] S.F. Dowell, "Seasonal Variation in Host Susceptibility
and Cycles of Certain Infectious Disease", Emerg. Infect.Dis.,
vol.7, no.3, 2002, pp.369-373.
[2] J.Brownlee, "An investigation into the periodicity of measles
epidemics in London from 1703 to the present day by the method
of the periodiogram.", Phil. Trans. Roy. Soc.London B, vol.208,
1918, pp. 225-250.
[3] R.J. Nelson ,and D.L.Drasen, "Melatonin mediates seasonal
adjustments in immune function", Res.Nutr.Dev., vol.39, no.3,
1999, pp.383-398.
[4] S.F.Dowell, C.G.Whitney, C.Wright, C.E.Rose, and
Jr,Schuchat, "Seasonal patterns of invasive pneumococcal disease",
Emerg. Infect. Dis., vol. 9, no.5, 2003, pp. 573-579.
[5] G.Blanc, and J.Caminopetroa, "Researches experiments surla dengue",
Ann. Inst. Pasteur., vol.44, 1930, pp.367- 436.
[6] S.Hales, P.Weinstein, and A.Woodward, "Dengue Fever Epidemic
in the South Pacific driven by El Nino Southern Oscillation", Lancet ,
vol. 348, 1996, pp.1664-1665.
[7] R.Anderson, B.T.Greenfell , and R.M.May, " Oscillatory fluctuations
in the incidence of infectious disease and the impact of vaccination:
time series analysis", J.Hyg.Camb, vol.93, 1984, pp. 587-608.
[8] N.M.Ferguson, D.J.Nokes, R.M.Anderson, "Dynamical complexity in
age-structure models of transmission of the measles virus:
Epidemiological implications at highlevels of vaccine uptake", Math.
Biosci. , vol..138, 1996., pp.101-130.
[9] D.M.Watts, D.S.Burke, B.A.Harrison, R.E.Whitmire, and A. Nisalak,
"Effect of temperature on the vector Efficiency of Aedes aegypti for
dengue 2 virus ", Am.J.Trop.Med.Hyg., vol.36, 1987, pp. 143-152.
[10] WHO, Dengue hemorrhagic fever, diagnosis, treatment and control.
World Health Organization, Geneva, Switzerland, 1986.
[11] D.J.Gubler, "Dengue hemorrhagic Fever", Clin.Microbiol.Rev.,
vol.11, 1998, pp. 480-491.
[12] D.S.Burke, A.Nisalak, D.Johnson, and R.M.Scott, " A prospective
study of dengue infections in Bangkok", Am. J.Trop. Med. Hyg., vol.
38, 1988, pp.172-180.
[13] G.Kuri , P..Mas, M.Soler, A.Goyenechea, and L.Morier, "Dengue
hemorrhagic fever in Cuba, 1981: rapid Diagnosis of the etiologic
agent", Bull. Pan. Am. Health. Org., vol.17, 1983, pp.126-132.
[14] J.E.Marsden, and M.McCraken, The Hopf bifurcation and its
application. Springer-Verlag(New York), 1976.
[15] D.W.Vanghn, S.Green, S.Kalayanarooj, B.L.Innis, S.Nimmannitya,
A.Santayakorn, and et al, "Dengue in the early febrile phase, viremia
and antibody responses", J.Inf.Dis., vol.176, 1997, pp..322-330.
[16] S.Gupta, J.Swinton, and R.M.Anderson, "Theoretical studies of
the effects of heterogeneity in the parasite population on the
transmission dynamics of malaria", Proc.Roy.Soc.London B, vol.256,
1994, pp. 231-238.
[17] M.Yasuno, and R.J.Tonn, "A study of the biting habits of Aedes
aegypti in Bangkok", Bull World Health Organ. vol.43, 1970,
319-325.
[18] L.F.Olsen ,G.L.Trusty, and W.M.Schaffer, "Oscillation and Chaos in
epidemics: a nonlinear dynamics study of six childhood diseases in
Copenhagen, Denmark", Theor. Populat. Biol., vol.33, 1988, pp. 344-
370.
[19] S.Gakkhar, and R.K.Naji , "Chaos in seasonally perturbed ratiodependent
prey-predator system", Chaos, Solitons & Fractals, vol.18,
2003, pp.107-118.
[20] S.Gakkhar, and R.K.Naji, "Seasonally perturbed prey-predator system
with predator-dependent functional response ", Chaos, Solitons &
fractals, vol.18, 2003, pp. 1075-1083.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56909", author = "Puntani Pongsumpun and I-Ming Tang", title = "Effect of the Seasonal Variation in the Extrinsic Incubation Period on the Long Term Behavior of the Dengue Hemorrhagic Fever Epidemic", abstract = "The incidences of dengue hemorrhagic disease (DHF)
over the long term exhibit a seasonal behavior. It has been
hypothesized that these behaviors are due to the seasonal climate
changes which in turn induce a seasonal variation in the incubation
period of the virus while it is developing the mosquito. The standard
dynamic analysis is applied for analysis the Susceptible-Exposed-
Infectious-Recovered (SEIR) model which includes an annual
variation in the length of the extrinsic incubation period (EIP). The
presence of both asymptomatic and symptomatic infections is
allowed in the present model. We found that dynamic behavior of the
endemic state changes as the influence of the seasonal variation of
the EIP becomes stronger. As the influence is further increased, the
trajectory exhibits sustained oscillations when it leaves the chaotic
region.", keywords = "Chaotic behavior, dengue hemorrhagic fever,extrinsic incubation period, SEIR model.", volume = "1", number = "10", pages = "478-7", }
