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.
Abstract: Dengue virus is transmitted from person to person
through the biting of infected Aedes Aegypti mosquitoes. DEN-1,
DEN-2, DEN-3 and DEN-4 are four serotypes of this virus. Infection
with one of these four serotypes apparently produces permanent
immunity to it, but only temporary cross immunity to the others. The
length of time during incubation of dengue virus in human and
mosquito are considered in this study. The dengue patients are
classified into infected and infectious classes. The infectious human
can transmit dengue virus to susceptible mosquitoes but infected
human can not. The transmission model of this disease is formulated.
The human population is divided into susceptible, infected, infectious
and recovered classes. The mosquito population is separated into
susceptible, infected and infectious classes. Only infectious
mosquitoes can transmit dengue virus to the susceptible human. We
analyze this model by using dynamical analysis method. The
threshold condition is discussed to reduce the outbreak of this
disease.