Epidemic spreading with migration in networked metapopulation.

Migration plays a crucial role in epidemic spreading, and its dynamic can be studied by metapopulation model. Instead of the uniform mixing hypothesis, we adopt networked metapopulation to build the model of the epidemic spreading and the individuals' migration. In these populations, individuals are connected by contact network and populations are coupled by individuals migration. With the network mean-field and the gravity law of migration, we establish the N-seat intertwined SIR model and obtain its basic reproduction number ℛ 0 . Meanwhile, we devise a non-markov Node-Search algorithm for model statistical simulations. Through the static network migration ansatz and ℛ 0 formula, we discover that migration will not directly increase the epidemic replication capacity. But when ℛ 0 > 1 , the migration will make the susceptive population evolve from metastable state (disease-free equilibrium) to stable state (endemic equilibrium), and then increase the influence area of epidemic. Re-evoluting the epidemic outbreak in Wuhan, top 94 cities empirical data validate the above mechanism. In addition, we estimate that the positive anti-epidemic measures taken by the Chinese government may have reduced 4 million cases at least during the first wave of COVID-19, which means those measures, such as the epidemiological investigation, nucleic acid detection in medium-high risk areas and isolation of confirmed cases, also play a significant role in preventing epidemic spreading after travel restriction between cities.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms.

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.