No abstract

Both the threat of bioterrorism and the natural emergence of contagious diseases underscore the importance of quantitatively understanding disease transmission in structured human populations. Over the last few years, researchers have advanced the mathematical theory of scale-free networks and used such theoretical advancements in pilot epidemic models. Scale-free contact networks are particularly interesting in the realm of mathematical epidemiology, primarily because these networks may allow meaningfully structured populations to be incorporated in epidemic models at moderate or intermediate levels of complexity. Moreover, a scale-free contact network with node degree correlation is in accord with the well-known preferred mixing concept. The present author describes a semi-empirical and deterministic epidemic modeling approach that (a) focuses on time-varying rates of disease transmission in both unstructured and structured populations and (b) employs probability density functions to characterize disease progression and outbreak controls. Given an epidemic curve for a historical outbreak, this modeling approach calls for Monte Carlo calculations (that define the average new infection rate) and solutions to integro-differential equations (that describe outbreak dynamics in an aggregate population or across all network connectivity classes). Numerical results are obtained for the 2003 SARS outbreak in Taiwan and the dynamical implications of time-varying transmission rates and scale-free contact networks are discussed in some detail.

A thin cylinder above a finitely conducting half-space is illuminated by a monochromatic plane wave. The electric vector of the incident plane wave is parallel to the axis of the cylinder and the Poynting vector of this incident plane wave intersects the surface of the finitely conducting half-space at an oblique angle. An imperfect image is used to derive the total current on the thin cylinder and the electric field at the surface of the half-space. The total induced current on the thin cylinder is shown to reduce to the appropriate limiting form when the height or the half-space conductivity becomes infinite.

No abstract

No abstract