MPSTAN: Metapopulation-Based Spatio-Temporal Attention Network for Epidemic Forecasting.

Accurate epidemic forecasting plays a vital role for governments to develop effective prevention measures for suppressing epidemics. Most of the present spatio-temporal models cannot provide a general framework for stable and accurate forecasting of epidemics with diverse evolutionary trends. Incorporating epidemiological domain knowledge ranging from single-patch to multi-patch into neural networks is expected to improve forecasting accuracy. However, relying solely on single-patch knowledge neglects inter-patch interactions, while constructing multi-patch knowledge is challenging without population mobility data. To address the aforementioned problems, we propose a novel hybrid model called metapopulation-based spatio-temporal attention network (MPSTAN). This model aims to improve the accuracy of epidemic forecasting by incorporating multi-patch epidemiological knowledge into a spatio-temporal model and adaptively defining inter-patch interactions. Moreover, we incorporate inter-patch epidemiological knowledge into both model construction and the loss function to help the model learn epidemic transmission dynamics. Extensive experiments conducted on two representative datasets with different epidemiological evolution trends demonstrate that our proposed model outperforms the baselines and provides more accurate and stable short- and long-term forecasting. We confirm the effectiveness of domain knowledge in the learning model and investigate the impact of different ways of integrating domain knowledge on forecasting. We observe that using domain knowledge in both model construction and the loss function leads to more efficient forecasting, and selecting appropriate domain knowledge can improve accuracy further.

A Two-Phase Feature Selection Method for Identifying Influential Spreaders of Disease Epidemics in Complex Networks.

Network epidemiology plays a fundamental role in understanding the relationship between network structure and epidemic dynamics, among which identifying influential spreaders is especially important. Most previous studies aim to propose a centrality measure based on network topology to reflect the influence of spreaders, which manifest limited universality. Machine learning enhances the identification of influential spreaders by combining multiple centralities. However, several centrality measures utilized in machine learning methods, such as closeness centrality, exhibit high computational complexity when confronted with large network sizes. Here, we propose a two-phase feature selection method for identifying influential spreaders with a reduced feature dimension. Depending on the definition of influential spreaders, we obtain the optimal feature combination for different synthetic networks. Our results demonstrate that when the datasets are mildly or moderately imbalanced, for Barabasi-Albert (BA) scale-free networks, the centralities' combination with the two-hop neighborhood is fundamental, and for Erdos-Rényi (ER) random graphs, the centralities' combination with the degree centrality is essential. Meanwhile, for Watts-Strogatz (WS) small world networks, feature selection is unnecessary. We also conduct experiments on real-world networks, and the features selected display a high similarity with synthetic networks. Our method provides a new path for identifying superspreaders for the control of epidemics.

The Efficacy of Urinary Continence in Patients Undergoing Robot-Assisted Radical Prostatectomy with Bladder-Prostatic Muscle Reconstruction and Bladder Neck Eversion Anastomosis.

Background and Objectives: To evaluate the efficacy of bladder-prostatic muscle reconstruction and bladder neck eversion anastomosis in the recovery of urinary continence after robot-assisted radical prostatectomy (RARP). Materials and Methods: From January 2020 to May 2022, 69 patients who underwent RARP in our hospital were recruited. Thirty-seven patients underwent RARP with the Veil of Aphrodite technique (control group). On the basis of the control group, 32 patients underwent bladder-prostatic muscle reconstruction and bladder neck eversion anastomosis during RARP (observation group). The recovery of urinary continence was followed up at 24 h and 1, 4, 12, and 24 weeks after catheter removal. Results: There were no significant differences in operative time (127.76 ± 21.23 min vs. 118.85 ± 24.71 min), blood loss (118.27 ± 16.75 mL vs. 110.77 ± 19.63 mL), rate of leakage (3.13% vs. 2.70%), rate of positive surgical margin (6.25% vs. 10.81%), or postoperative Gleason score [7 (6−8) vs. 7 (7−8)] between the observation group and the control group (p > 0.05). After catheter removal, the rates of urinary continence at 24 h, 1 week, 4 weeks, 12 weeks, and 24 weeks were 46.88%, 68.75%, 84.38%, 90.63%, and 93.75% in the observation group, respectively. Meanwhile, the rates of urinary continence in the control group were 21.62%, 37.84%, 62.16%, 86.49%, and 91.89%, respectively. There was a significant difference between the two groups (p = 0.034), especially at 24 h, 1 week, and 4 weeks after catheter removal (p < 0.05). Conclusions: Bladder-prostatic muscle reconstruction and bladder neck eversion anastomosis were beneficial to the recovery of urinary continence after RARP, especially early urinary continence.

Risk perception and subsidy policy-based voluntary vaccination driven by multiple information sources.

Exploring vaccination behavior is fundamental to understand the role of vaccine in suppressing the epidemic. Motivated by the efficient role of the risk perception and the subsidy policy in promoting vaccination, we propose the Risk Perception and the Risk Perception with Subsidy Policy voluntary vaccination strategies with imperfect vaccine. The risk perception is driven by multiple information sources based on global information (released by Public Health Bureau) and local information (from first-order neighbors). In time-varying networks, we use the mean-field approach and the Monte Carlo simulations to analyze the epidemic dynamics under vaccination behavior with imperfect vaccine. We find that vaccination with the incorporation of risk perception and subsidy policy can effectively control the epidemic. Moreover, information from different sources plays different roles. Global information is more helpful in promoting vaccination than local information. In addition, to further understand the influence of vaccination strategies, we calculate the social cost as the cost for the vaccine and treatment, and find that excess vaccination cost results in a higher social cost after the herd immunity. Thus, for balancing the epidemic control and social cost, providing individuals with more global information as well as local information would be helpful in vaccination. These results are expected to provide insightful guidance for designing the policy to promote vaccination.

Application of single-point prostate biopsy in elderly patients with highly suspected prostate cancer.

Objective: To explore the feasibility of single-point prostate biopsy in elderly patients with highly suspected prostate cancer. Methods: Forty-three patients with a prostate imaging reporting and data system score (PI-RADS) of 5, age ≥ 80 years and/or PSA ≥ 100 ng/ml and/or Eastern Cooperative Oncology Group score ≥ 2 were enrolled in our hospital from March 2020 to June 2022. Targeted surgery of these patients was performed using only precise local anesthesia in the biopsy area. The biopsy tissues were examined by intraoperative frozen section examination (IFSE). If the result of IFSE was negative, traditional systematic biopsy and further routine pathological examination were performed. The positive rate of biopsy, operation time, complications and pain score were recorded. Results: The positive rate of prostate biopsy was 94.7%. The results of IFSE in two patients were negative, and the routine pathological results of further systematic biopsy of those patients were also negative. The visual analog scale and visual numeric scale were 2 (2-4) and 3 (2-3), respectively, during the biopsy procedure. The mean time of operation was 8.5 ± 2.1 min from the beginning of anesthesia to the end of biopsy. It took 35.3 ± 18.7 minutes to obtain the pathological report of IFSE. The incidences of complication hematuria and urinary retention were 10.5% and 2.6%, respectively. Conclusion: For elderly patients with highly suspected prostate cancer, single-point prostate biopsy can be used to quickly and safely obtain pathological results.

Center-environment feature models for materials image segmentation based on machine learning.

Materials properties depend not only on their compositions but also their microstructures under various processing conditions. So far, the analyses of complex microstructure images rely mostly on human experience, lack of automatic quantitative characterization methods. Machine learning provides an emerging vital tool to identify various complex materials phases in an intelligent manner. In this work, we propose a "center-environment segmentation" (CES) feature model for image segmentation based on machine learning method with environment features and the annotation input of domain knowledge. The CES model introduces the information of neighbourhood as the features of a given pixel, reflecting the relationships between the studied pixel and its surrounding environment. Then, an iterative integrated machine learning method is adopted to train and correct the image segmentation model. The CES model was successfully applied to segment seven different material images with complex texture ranging from steels to woods. The overall performance of the CES method in determining boundary contours is better than many conventional methods in the case study of the segmentation of steel image. This work shows that the iterative introduction of domain knowledge and environment features improve the accuracy of machine learning based image segmentation for various complex materials microstructures.

Intervention of resource allocation strategies on spatial spread of epidemics.

Medical resources are crucial in mitigating epidemics, especially during pandemics such as the ongoing COVID-19. Thereby, reasonable resource deployment inevitably plays a significant role in suppressing the epidemic under limited resources. When an epidemic breaks out, people can produce resources for self-protection or donate resources to help others for treatment. That is, the exchange of resources also affects the transmission between individuals, thus, altering the epidemic dynamics. To understand factors on resource deployment and the interplay between resource and transmission we construct a metapopulation network model with resource allocation. Our results indicate actively or promptly donating resources is not helpful to suppress the epidemic under both homogeneous population distribution and heterogeneous population distribution. Besides, strengthening the speed of resources production can significantly increase the recovery rate so that they reduce the final outbreak size. These results may provide policy guidance toward epidemic containment.

Intervention strategies for epidemic spreading on bipartite metapopulation networks.

Intervention strategies are of great significance for controlling large-scale outbreaks of epidemics. Since the spread of epidemic depends largely on the movement of individuals and the heterogeneity of the network structure, understanding potential factors that affect the epidemic is fundamental for the design of reasonable intervention strategies to suppress the epidemic. So far, most of previous studies mainly consider intervention strategies on the network composed of a single type of locations, while ignoring the movement behavior of individuals to and from locations that are composed of different types, i.e., residences and public places, which often presents heterogeneous structure. In addition, the transmission rate in public places with different population flows is heterogeneous. Inspired by the above observation, we build a bipartite metapopulation network model and propose intervention strategies based on the importance of public places. With the Markovian Chain approach, we derive the epidemic threshold under intervention strategies. Experimental results show that, compared with the uniform intervention to residences or public places, nonuniform intervention to public places is more effective for suppressing the epidemic with an increased epidemic threshold. Specifically, interventions to public places with large degree can further suppress the epidemic. Our study opens a new path for understanding the spatial epidemic spread and provides guidance for the design of intervention strategies for epidemics in the future.

The Application of Biopsy Density in Transperineal Templated-Guided Biopsy Patients With PI-RADS<3.

Background: In patients with multiparameter magnetic resonance imaging (mpMRI) low-possibility but highly clinical suspicion of prostate cancer, the biopsy core is unclear. Our study aims to introduce the biopsy density (BD; the ratio of biopsy cores to prostate volume) and investigates the BD-predictive value of prostate cancer and clinically significant prostate cancer (csPCa) in PI-RADS<3 patients. Methods: Patients underwent transperineal template-guided prostate biopsy from 2012 to 2022. The inclusion criteria were PI-RADS<3 with a positive digital rectal examination or persistent PSA abnormalities. BD was defined as the ratio of the biopsy core to the prostate volume. Clinical data were collected, and we grouped the patients according to pathology results. Kruskal-Wallis test and chi-square test were used in measurement and enumeration data, respectively. Logistics regression was used to choose the factor associated with positive biospy and csPCa. The receiver operating characteristic (ROC) curve was used to evaluate the ability to predict csPCa. Results: A total of 115 patients were included in our study. Biopsy was positive in 14 of 115 and the International Society of Urological Pathology grade groups 2-5 were in 7 of all the PCa patients. The BD was 0.38 (0.24-0.63) needles per milliliter. Binary logistics analysis suggested that PSAD and BD were correlated with positive biopsy. Meanwhile, BD and PSAD were associated with csPCa. The ROC curve illustrated that BD was a good parameter to predict csPCa (AUC=0.80, 95% CI: 0.69-0.91, p<0.05). The biopsy density combined with PSAD increased the prediction of csPCa (AUC=0.90, 95% CI: 0.85-0.97, p<0.05). The cut-off value of the BD was 0.42 according to the Youden index. Conclusion: In PI-RADS<3 patients, BD and PSAD are related to csPCa. A biopsy density of more than 0.42 needles per millimeter can increase the csPCa detection rate, which should be considered as an alternative biopsy method when we perform prostate biopsy in patients with PI-RADS<3.

Factor Analysis and Regression Prediction Model of Swimmers' Performance Structure Based on Mixed Genetic Neural Network.

With the development of economy, people put forward higher demands on material life and spiritual life, and sports have become an indispensable part of daily life. Ten km freestyle, although it has been started late, is loved by people all over the world, and it is getting more and more attention in the world of competitive sports. Through the theoretical research of 10 km freestyle, it can be seen that most of the research on this project is focused on the training, selection of materials, and how to improve the technique of crossing obstacles or pools, while the research on the performance of 10 km freestyle is limited to the analysis of the development trend of the performance and no research on the prediction of the actual performance, which to some extent restricts the scientific development of 10 km freestyle. The efficiency of a suitable learning is a factor that influences whether the training and learning of a BP neural network is stable or not. It can also directly determine the choice of weights. When the learning rate is chosen to be large, it increases the speed of learning and makes the stability of the network change. This has limited the scientific development of 10 km freestyle to a certain extent, and it is also a good entry point for the research of 10 km freestyle. BP neural network is one of the most widely used neural network models, which can be used for classification, clustering, prediction, and other related problems. In this study, we propose a comprehensive evaluation method of 10 km freestyle performance based on BP neural network and try to establish a neural network evaluation model by combining the athletes' physiological and biochemical indexes and sports performance. In this study, the normalized index values are used as the network input, and the athletes' performance in 10 km freestyle is used as the network output to predict the athletes' performance in 10 km freestyle. This study provides a theoretical basis for adjusting the condition of 10 km freestyle athletes and improving their performance. Optimize the reasonable allocation of resources between coaches and athletes, and increase the opportunities for coaches and athletes to communicate and learn from outside.

The application of intraoperative frozen section examination in multiparametric magnetic resonance imaging/transrectal ultrasound fusion prostate biopsy during a major pandemic.

Background: To investigate the value of intraoperative frozen section examination (IFSE) in multiparametric magnetic resonance imaging/transrectal ultrasound (mpMRI/TRUS) fusion prostate biopsy in a major pandemic. Methods: A total of 35 patients were prospectively enrolled in our hospital from March 2020 to January 2021. The mpMRI/TRUS fusion system was used to perform a targeted biopsy, and the collected specimens were examined by IFSE (Observation Group 1). Then, a targeted biopsy was performed again for routine pathological examination (Observation Group 2). Finally, a systemic biopsy was performed, and the obtained specimens were routinely examined (Control Group). The positive rate, single core positive rate, Gleason score, and time to obtain pathological reports were compared between the groups. Results: The positive rate was 48.6% (17/35) in the control group, 48.6% (17/35) in Observation Group 1, and 51.4% (18/35) in Observation Group 2, showing no significant difference (P>0.05). The single core positive rates were 17.8%, 44.6%, and 47.1% in the Control Group, Observation Group 1, and Observation Group 2, respectively. Observation Group 1 and Observation Group 2 were significantly different from the Control Group (P<0.001). No participants in Observation Group 1 had increased or decreased Gleason scores compared with those in Observation Group 2. The time to obtain the pathological report was 0.025±0.014 days and 4.216±1.073 days for Observation Group 1 and Observation Group 2, respectively, showing a significant difference (P<0.001). Conclusions: This study showed that IFSE can not only rapidly obtain the pathological report of an mpMRI/TRUS biopsy, but can also ensure the accuracy of the pathological diagnosis. Trial Registration: CHICTR, Identifier: ChiCTR2000040789. Registered 10 December 2020 - Retrospectively registered, http://www.chictr.org.cn/edit.aspx?pid=63252&htm=4.

Phase transition in the majority-vote model on time-varying networks.

Social interactions may affect the update of individuals' opinions. The existing models such as the majority-vote (MV) model have been extensively studied in different static networks. However, in reality, social networks change over time and individuals interact dynamically. In this work, we study the behavior of the MV model on temporal networks to analyze the effects of temporality on opinion dynamics. In social networks, people are able to both actively send connections and passively receive connections, which leads to different effects on individuals' opinions. In order to compare the impact of different patterns of interactions on opinion dynamics, we simplify them into two processes, that is, the single directed (SD) process and the undirected (UD) process. The former only allows each individual to adopt an opinion by following the majority of actively interactive neighbors, while the latter allows each individual to flip opinion by following the majority of both actively interactive and passively interactive neighbors. By borrowing the activity-driven time-varying network with attractiveness (ADA model), the two opinion update processes, i.e., the SD and the UD processes, are related with the network evolution. With the mean-field approach, we derive the critical noise threshold for each process, which is also verified by numerical simulations. Compared with the SD process, the UD process reaches a larger consensus level below the same critical noise. Finally, we also verify the main results in real networks.

Automatic detection of Kikuchi bands based on Radon transform and PPHT.

The information of crystal structure and orientation can be provided by analysing the EBSD (electron backscatter diffraction) patterns which are obtained with the EBSD devices. The reliability and accuracy of the information relies on the location of bands and intersections of the EBSD patterns. In this study, a method is proposed to automatically obtain the locations and intersections of the EBSD patterns, that is, Kikuchi bands. The proposed method uses Radon transform and progressive probabilistic Hough transform to detect straight lines and line segments of the Kikuchi band edges, respectively. Then, Kikuchi bands can be presented by fitting the hyperbolas with the endpoints of line segments. The results can numerically describe the information of Kikuchi bands. Experimental results show that the method is robust and can detect more accurate Kikuchi bands and intersections.

In this paper, a novel method is proposed to detect the electron backscatter diffraction patterns. Electron backscatter diffraction patterns are a class images consisting of multiple parallel lines of light and dark pairs. The bands on the image can reflect the information of crystal structure and orientation. Most existing methods are complex to implement and computationally intensive in detecting edges and intersections of bands. Therefore, we designed a fast and easy-to-implement detection method with relatively good accuracy to overcome the drawbacks of existing methods. Our method is based on straight line detection and line segment detection. After matching the straight line detection results and the line segment detection results, the edges are obtained by fitting the line segment endpoints using a hyperbola, and the intersections are obtained by using centerline positioning. Experiments have shown that our method has good accuracy and can detect less perfect patterns . In addition, our method is easy to implement and and is valuable for computationally constrained cases.

Application of 16 G Biopsy Needle in Transperineal Template-Guided Prostate Biopsy.

BACKGROUND: The aim of this study was to evaluate the clinical value of 16 G biopsy needle in transperineal template-guided prostate biopsy (TTPB), compared with 18 G biopsy needle. METHODS: The patients who underwent TTPB from August 2020 to February 2021 were randomized into 2 groups using a random number table. The control group (n = 65) and the observation group (n = 58) performed biopsy with 18 G (Bard MC l820) and 16 G (Bard MC l616) biopsy needles, respectively. Positive rate of biopsy, Gleason score, complications, and pain score were statistically analyzed. RESULTS: The age, prostate volume, PSA, and the number of cores were comparable between the 2 groups. The positive rate of biopsy in the observation group was 68.9% (40/58), meanwhile the control group was 46.2% (30/65). There was statistical difference between the 2 groups (p = 0.011). Gleason score of the observation group (8 [7-9]) was higher than that of the control group (8 [6-9]) (p = 0.038). There was no significant difference in pain score and complications including hematuria, hematospermia, perineal hematoma, infection, and urinary retention between the 2 groups (p > 0.05). CONCLUSIONS: 16 G biopsy needle significantly improved the positive rates and accurately evaluate the nature of lesions, meanwhile did not increase the incidence of complications compared with 18 G biopsy needle.

Impact of individual behavioral changes on epidemic spreading in time-varying networks.

Changes in individual behavior often entangle with the dynamic interaction of individuals, which complicates the epidemic process and brings great challenges for the understanding and control of the epidemic. In this work, we consider three kinds of typical behavioral changes in epidemic process, that is, self-quarantine of infected individuals, self-protection of susceptible individuals, and social distancing between them. We connect the behavioral changes with individual's social attributes by the activity-driven network with attractiveness. A mean-field theory is established to derive an analytical estimate of epidemic threshold for susceptible-infected-susceptible models with individual behavioral changes, which depends on the correlations between activity, attractiveness, and the number of generative links in the susceptible and infected states. We find that individual behaviors play different roles in suppressing the epidemic. Although all the behavioral changes could delay the epidemic by increasing the epidemic threshold, self-quarantine and social distancing of infected individuals could effectively decrease the epidemic outbreak size. In addition, simultaneous changes in these behaviors and the timing of implement of them also play a key role in suppressing the epidemic. These results provide helpful significance for understanding the interaction of individual behaviors in the epidemic process.

Unclonable Micro-Texture with Clonable Micro-Shape towards Rapid, Convenient, and Low-Cost Fluorescent Anti-Counterfeiting Labels.

An ideal anti-counterfeiting label not only needs to be unclonable and accurate but also must consider cost and efficiency. But the traditional physical unclonable function (PUF) recognition technology must match all the images in a database one by one. The matching time increases with the number of samples. Here, a new kind of PUF anti-counterfeiting label is introduced with high modifiability, low reagent cost (2.1 × 10-4 USD), simple and fast authentication (overall time 12.17 s), high encoding capacity (2.1 × 10623 ), and its identification software. All inorganic perovskite nanocrystalline films with clonable micro-profile and unclonable micro-texture are prepared by laser engraving for lyophilic patterning, liquid strip sliding for high throughput droplet generation, and evaporative self-assembling for thin film deposition. A variety of crystal film profile shapes can be used as "specificator" for image recognition, and the verification time of recognition technology based on this divide-and-conquer strategy can be decreased by more than 20 times.

Modeling of suppression and mitigation interventions in the COVID-19 epidemics.

BACKGROUND: The global spread of the COVID-19 pandemic has become the most fundamental threat to human health. In the absence of vaccines and effective therapeutical solutions, non-pharmaceutic intervention has become a major way for controlling the epidemic. Gentle mitigation interventions are able to slow down the epidemic but not to halt it well. While strict suppression interventions are efficient for controlling the epidemic, long-term measures are likely to have negative impacts on economics and people's daily live. Hence, dynamically balancing suppression and mitigation interventions plays a fundamental role in manipulating the epidemic curve. METHODS: We collected data of the number of infections for several countries during the COVID-19 pandemics and found a clear phenomenon of periodic waves of infection. Based on the observation, by connecting the infection level with the medical resources and a tolerance parameter, we propose a mathematical model to understand impacts of combining intervention measures on the epidemic dynamics. RESULTS: Depending on the parameters of the medical resources, tolerance level, and the starting time of interventions, the combined intervention measure dynamically changes with the infection level, resulting in a periodic wave of infections controlled below an accepted level. The study reveals that, (a) with an immediate, strict suppression, the numbers of infections and deaths are well controlled with a significant reduction in a very short time period; (b) an appropriate, dynamical combination of suppression and mitigation may find a feasible way in reducing the impacts of epidemic on people's live and economics. CONCLUSIONS: While the assumption of interventions deployed with a cycle of period in the model is limited and unrealistic, the phenomenon of periodic waves of infections in reality is captured by our model. These results provide helpful insights for policy-makers to dynamically deploy an appropriate intervention strategy to effectively battle against the COVID-19.

A Path-Based Distribution Measure for Network Comparison.

As network data increases, it is more common than ever for researchers to analyze a set of networks rather than a single network and measure the difference between networks by developing a number of network comparison methods. Network comparison is able to quantify dissimilarity between networks by comparing the structural topological difference of networks. Here, we propose a kind of measures for network comparison based on the shortest path distribution combined with node centrality, capturing the global topological difference with local features. Based on the characterized path distributions, we define and compare network distance between networks to measure how dissimilar the two networks are, and the network entropy to characterize a typical network system. We find that the network distance is able to discriminate networks generated by different models. Combining more information on end nodes along a path can further amplify the dissimilarity of networks. The network entropy is able to detect tipping points in the evolution of synthetic networks. Extensive numerical simulations reveal the effectivity of the proposed measure in network reduction of multilayer networks, and identification of typical system states in temporal networks as well.

Network structure-based interventions on spatial spread of epidemics in metapopulation networks.

Mathematical modeling of epidemics is fundamental to understand the mechanism of the disease outbreak and provides helpful indications for effectiveness of interventions for policy makers. The metapopulation network model has been used in the analysis of epidemic dynamics by taking individual migration between patches into account. However, so far, most of the previous studies unrealistically assume that transmission rates within patches are the same, neglecting the nonuniformity of intervention measures in hindering epidemics. Here, based on the assumption that interventions deployed in a patch depend on its population size or economic level, which have shown a positive correlation with the patch's degree in networks, we propose a metapopulation network model to explore a network structure-based intervention strategy, aiming at understanding the interplay between intervention strategy and other factors including mobility patterns, initial population, as well as the network structure. Our results demonstrate that interventions to patches with different intensity are able to suppress the epidemic spreading in terms of both the epidemic threshold and the final epidemic size. Specifically, the intervention strategy targeting the patches with high degree is able to efficiently suppress epidemics. In addition, a detrimental effect is also observed depending on the interplay between the intervention measures and the initial population distribution. Our study opens a path for understanding epidemic dynamics and provides helpful insights into the implementation of countermeasures for the control of epidemics in reality.

Random walks in time-varying networks with memory.

Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. An individual's memory has been proved to be crucial to affect network evolution and dynamical processes unfolding on the network. In this work, we study the random-walk process on an extended activity-driven network model by taking account of an individual's memory. We analyze how an individual's memory affects random-walk process unfolding on the network when the timescales of the processes of the random walk and the network evolution are comparable. Under the constraints of long-time evolution, we derive analytical solutions for the distribution of walkers at the stationary state and the mean first-passage time of the random-walk process. We find that, compared with the memoryless activity-driven model, an individual's memory enhances the activity fluctuation and leads to the formation of small clusters of mutual contacts with high activity nodes, which reduces a node's capability of gathering walkers, especially for the nodes with large activity, and memory also delays the mean first-passage time. The results on real networks also support the theoretical analysis and numerical results with artificial networks.