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.

Honeybees have an irreplaceable position in agricultural production and the stabilization of natural ecosystems. Unfortunately, honeybee populations have been declining globally. Parasites, diseases, poor nutrition, pesticides, and climate changes contribute greatly to the global crisis of honeybee colony losses. Mathematical models have been used to provide useful insights on potential factors and important processes for improving the survival rate of colonies. In this review, we present various mathematical tractable models from different aspects: 1) simple bee-only models with features such as age segmentation, food collection, and nutrient absorption; 2) models of bees with other species such as parasites and/or pathogens; and 3) models of bees affected by pesticide exposure. We aim to review those mathematical models to emphasize the power of mathematical modeling in helping us understand honeybee population dynamics and its related ecological communities. We also provide a review of computational models such as VARROAPOP and BEEHAVE that describe the bee population dynamics in environments that include factors such as temperature, rainfall, light, distance and quality of food, and their effects on colony growth and survival. In addition, we propose a future outlook on important directions regarding mathematical modeling of honeybees. We particularly encourage collaborations between mathematicians and biologists so that mathematical models could be more useful through validation with experimental data.