Spatial spread of infectious diseases among populations via the mobility of humans is highly stochastic and heterogeneous. Accurate forecast/mining of the spread process is often hard to be achieved by using statistical or mechanical models. Here we propose a new reverse problem, which aims to identify the stochastically spatial spread process itself from observable information regarding the arrival history of infectious cases in each subpopulation. We solved the problem by developing an efficient optimization algorithm based on dynamical programming, which comprises three procedures: 1) anatomizing the whole spread process among all subpopulations into disjoint componential patches; 2) inferring the most probable invasion pathways underlying each patch via maximum likelihood estimation; and 3) recovering the whole process by assembling the invasion pathways in each patch iteratively, without burdens in parameter calibrations and computer simulations. Based on the entropy theory, we introduced an identifiability measure to assess the difficulty level that an invasion pathway can be identified. Results on both artificial and empirical metapopulation networks show the robust performance in identifying actual invasion pathways driving pandemic spread.

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example and calculate conditions of herd immunity for multiple vaccines and disease variants. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced if vaccination were available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral, Delta, and Omicron strains. Numerical results demonstrate that the static herd immunity threshold corresponds to one percent of the population requiring hospitalization or isolation at some point in time. We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered while still maintaining the same proportion of cumulative hospitalized/isolated individuals.

Understanding how infectious diseases spatially diffuse is critical to predict and control the epidemic prevalence. However, uncovering epidemic spatial invasion is challenging due to stochastic travel of hosts and insufficient data availability. In this study, we develop a methodology for inferring global invasion pathways on metapopulation networks with the susceptible-infected-recovered (SIR) epidemics. To solve the inference problem, we infer the invasion pathways of each invasion case as a subgraph containing a part of global invasion pathways at each epidemic arrival time. We first develop a reduction approach to decrease the sizes of the dominant invasion cases, and propose a local optimization method aiming at the SIR epidemics based on epidemic maximum diffusion (EMD) to infer spatial invasion pathways of the reduced invasion cases, and reconstruct the global invasion pathways. Compared with the previous work, we reduce the computational complexity of invasion cases, and improve the calculation of epidemic diffusion likelihood and effectiveness of the algorithm for epidemic recovery. Simulations on real and synthetic metapopulation networks verify the validity of our algorithm. Finally, an empirical example of the 2009 A (H1N1) in the USA is presented to uncover the spatial invasion pathways and identify the superinvaders.

The co-evolution of epidemic and information spread within multilayer networks is a current hot topic in network science. During epidemic outbreaks, the accompanying information exhibits both outbreak and reception game behaviors; yet, these complex phenomena have been scarcely addressed in existing research. In this paper, we model information outbreaks using activated individuals who transmit messages to their neighbors, while also considering the game behaviors of information receivers. By focusing on these two factors, we establish a multilayer network model featuring both information outbreaks and reception games. Employing the microscopic Markov chain method, we analyze the propagation dynamics within this network and derive epidemic thresholds, corroborating these results with Monte Carlo simulations. Our findings indicate that information outbreaks suppress epidemic outbreaks, whereas increased costs of information reception promote epidemic spread. Smooth information dissemination further inhibits the transmission of the epidemic. Additionally, we observe that heterogeneity in the network structure between the virtual and physical layers reduces the ultimate scale of epidemic infection, with the virtual layer exerting a more substantial influence. These insights are crucial for elucidating the co-evolutionary mechanisms of spread within multilayer networks and for developing effective epidemic prevention and control strategies.

The identification of influential nodes in multilayer networks is a rapidly growing area in network science. However, insufficient consideration of both inter- and intra-layer weights in existing research has limited the effectiveness of node identification methods. To address this gap, we propose a novel algorithm, coupling weighted intra-layer and inter-layer influence factors (CWIIIF), which accurately identifies nodes that exert significant influence in multilayer networks. The algorithm integrates weighted intra- and inter-layer influence factors, taking into account the unique properties of multilayer network structures. First, we define a set of layer weight influence parameters, including active nodes, active paths, and communication intersections between layers, to determine the weight of each network layer. We then calculate the intra-layer influence of each node using a combination of K-shell and betweenness centrality methods. Finally, we introduce a set of coupled equations that convert the intra-layer influence vectors into scalar values by incorporating the weights of each layer, producing a final influence score for each node. To validate the effectiveness of our algorithm, we conducted four comparative experiments across nine real-world and one synthetic multilayer networks. The results demonstrate that our algorithm significantly outperforms nine classical and state-of-the-art methods for identifying influential nodes.