Impacts of Periodic Delays and Vertical Transmission on the Dynamics of Dengue Fever

Dengue disease is a serious problem in the subtropical and tropical regions of the world, including Taiwan. It is transmitted to humans by the bite of Aedes mosquitoes, and four serotypes have been identified. The control of the spread of the disease is an important issue in the public health due to the high infection rate of dengue fever and high death rate of its dengue hemorrhagic fever. In this project, we shall propose systems of delay differential equations with a periodic time delay and reaction-diffusion systems with periodic delays (the incubation period) describing the influence of temperature-dependent delays, the seasonal fluctuations, the vertical transmission in mosquitoes, and the spatial heterogeneity on dengue fever transmission. We shall first define the associated reproduction number(s), and show that the global dynamics (extinction/persistence) of disease can be determined by the reproduction number(s) by using the theory of uniform persistence.

Project ID:PB10901-3076
External Project ID:MOST108-2115-M182-001-MY3