The scale-free network behavior of ambient volatile organic compounds.

A scale-free network model with surface and vertical field measurements was used to identify the connectivity distribution of the scale-free network behavior of ambient volatile organic compounds (VOCs). The results show that the carbon number (C(n)) with the total amount of C(n) compounds (P(C(n))) possesses an explicit relationship with the scale-free network behavior. The proportionate coefficient (α) and exponent (γ) of the scale-free network model with spatial and temporal variations are estimated and discussed. The analytical results demonstrate that although photochemical reactions cause the VOCs fraction variation, they do not alter the fraction of C(n) compounds observably. Therefore, the values of α and of γ did not vary with time, but with local regional characteristics. The results indicate that the influence of local VOCs emissions occurs at a height of 100 m, but becomes insufficient at a height of 300 m. Air mass mixing increases with greater height; thus, the influence of regional characteristics at a height of 700 m is low. Finally, a successful empirical model was established to evaluate the distribution of surface VOCs in various regions.

A new scale-free network model for simulating and predicting epidemics.

The course of epidemics often resembles a scale-free network, but some specific elements should be considered in developing a new model. This study introduces a time-shifting and discontinuous forcing function H into the scale-free network model to fit the specific period and intensity of the infection, and redefines the probability p as abortive infection rate. For the non-human vectors or hosts, three new factors (new connectivity K(i)(t), new links M, and time delay τ) were introduced in the proposed model of this study. The simulation results of six types of epidemic transmissions show that the proposed Scale-Free Epidemic Models, SFE-1 and SFE-2, are accurate. SFE-1 model and SFE-2 model are useful for the transmission categories from human and insects/vertebrates, respectively. Further comparisons of different races/ethnicities and different transmission categories of AIDS cases in the United States were also analyzed. Both SFE models can be used to predict epidemics and can suggest the results more clearly, irrespective of whether the epidemics are under control. Therefore, the proposed SFE models can help the government determine the level of caution required and predict the results of policy decisions, thus helping to balance socioeconomic and health concerns.