The large volume of geotagged Twitter streaming data on flu epidemics provides chances for researchers to explore, model, and predict the trends of flu cases in a timely manner. However, the explosive growth of data from social media makes data sampling a natural choice. In this paper, we develop a method for influenza prediction based on the real-time tweet data from social media, and this method ensures real-time prediction and is applicable to sampling data. Specifically, we first simulate the sampling process of flu tweets, and then develop a specific partial differential equation (PDE) model to characterize and predict the aggregated flu tweet volumes. Our PDE model incorporates the effects of flu spreading, flu recovery, and active human interventions for reducing flu. Our extensive simulation results show that this PDE model can almost eliminate the data reduction effects from the sampling process: It requires lesser historical data but achieves stronger prediction results with a relative accuracy of over 90% on the 1% sampling data. Even for the more aggressive data sampling ratios such as 0.1% and 0.01% sampling, our model is still able to achieve relative accuracies of 85% and 83%, respectively. These promising results highlight the ability of our mechanistic PDE model in predicting temporal–spatial patterns of flu trends even in the scenario of small sampling Twitter data.

Specification of PM_2.5 transmission characteristics is important for pollution control and policymaking. We apply higher-order organization of complex networks to identify major potential PM_2.5 contributors and PM_2.5 transport pathways of a network of 189 cities in China. The network we create in this paper consists of major cities in China and contains information on meteorological conditions of wind speed and wind direction, data on geographic distance, mountains, and PM_2.5 concentrations. We aim to reveal PM_2.5 mobility between cities in China. Two major conclusions are revealed through motif analysis of complex networks. First, major potential PM_2.5 pollution contributors are identified for each cluster by one motif, which reflects movements from source to target. Second, transport pathways of PM_2.5 are revealed by another motif, which reflects transmission routes. To our knowledge, this is the first work to apply higher-order network analysis to study PM_2.5 transport.

Real-time and geo-tagged data on PM _2.5 enable researchers to model and predict the trends of air pollution effectively. On the basis of network and clustering, a specific advection partial differential equation (PDE) model is proposed to forecast the spatial-temporal dynamics of PM _2.5 concentration at large scale of city-cluster. The proposed PDE model incorporates the effects of advection, local emission and dispersion. The prediction is performed in real-time with varying model parameters for assessing the current situation. Good simulation results not only demonstrate the proposed PDE has good prediction ability, but also show that the model can quantify the advection and local effects for the air pollution of each city-cluster to some extent. Moreover, the methodology can be extended to other types of air pollution provided that data are available.

The emerging business models have impelled firms’ competition in a brand-new and fast-growing market. This study examines such a competition for market share through advertising and loyalty reward programs. Two stages can be distinguished based on the transformation of the competition strategies. These stages can be formulated as a dynamic differential game model and a static Hotelling game model. The operation strategies and performances of two firms are determined and compared via analytical studies and case analyses toward a bicycle-sharing program, i.e., Ofo versus Mobike. Historical data are used to fit the curve of the market size and to estimate the parameter values of these models. The results show that during the first stage, the difference in market share between these firms gradually decreases (increases) when the advertising response constant is low (high). Meanwhile, in the second stage, these firms offer converse reward strategies.

The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization of least squares misfit function. Firstly, the tensor train decomposition approach is presented as global convergence algorithm. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. Then the inverse problem solution is reached by implementation of the local gradient approach. The evident formula for the gradient of the misfit function is obtained. The inverse problem for the diffusive logistic mathematical model described online social networks is solved by combination of tensor train optimization and local gradient methods. The numerical results are presented and discussed.