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-ExposedInfectious-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.