Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distribution, and we develop a compartmental model using it to model the heterogeneity of contact rates in the population. We explore the transmission dynamics of the developed model using numerical simulations with different parameter settings, which characterize different levels of heterogeneity. The results show that when the reproductive number, R₀, is larger than one, a low level of heterogeneity results in dynamics similar to those predicted by the homogeneous mixing model. As the level of heterogeneity increases, the dynamics become more different. As a test case, we calibrated the model with the case incidence data for severe acute respiratory syndrome (SARS) in Beijing in 2003, and the estimated parameters demonstrated the effectiveness of the control measures taken during that period.

The Cropland Data Layer (CDL) product provides categorized land-cover information encompassing the whole contiguous United States. Using the latest Web and geospatial interoperability technologies, CropScape was built to visualize, query, disseminate, and analyze historical and current CDL data interactively and intuitively over the Internet. CropScape can be utilized as a useful online mapping educational tool and an important source of free geospatial data and geospatial Web services in GIS education. This article introduces the CDL product and functions of CropScape, and presents several specific examples of cropland exploring, thematic map creation, natural disaster assessment, crop planting patterns discovery, geospatial data mashup, and geospatial Web application development to demonstrate CropScape’s capabilities.