A method for enhancing epidemic prevention and management of infectious diseases through network modeling

By constructing random walk technology of heterogeneous graphs and meta-paths, combining risk factors, and using the word2vec model for node embedding and risk assessment, the problem that traditional methods are difficult to capture complex infectious disease transmission networks is solved, and efficient risk prediction and resource optimization are achieved.

CN119541893BActive Publication Date: 2025-10-14BEIHANG UNIV
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Patent Information

Application Number
CN202411676847.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-11-22
Publication Date
2025-10-14
Estimated Expiration
2044-11-22

AI Technical Summary

Technical Problem

Traditional infectious disease prevention and control management methods have difficulty capturing complex infectious disease transmission networks and ignore the impact of environmental factors and individual behavior, resulting in delayed responses and improper resource allocation.

Method used

A heterogeneous graph is constructed, and high-risk individuals and locations are evaluated through random walk and node embedding techniques of meta-paths, combined with risk factors. The word2vec model is used for node embedding and risk assessment.

Benefits of technology

It improves the accuracy of infectious disease transmission risk prediction, optimizes resource allocation, improves epidemic prevention and control efficiency, and reduces resource waste.

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Abstract

The present disclosure provides a kind of epidemic prevention and management method for enhancing infectious disease through network modeling.It includes four processes: first, according to the detailed epidemic contact information recorded in the survey report, an epidemic correlation graph is constructed;then, by defining a meta-path, a node sequence in a heterogeneous graph is generated using random walk to capture the semantic and structural correlation between multiple nodes in the heterogeneous graph;then, risk factors are introduced and adjusted, i.e.according to the risk factor level provided by the Center for Disease Control and Prevention, the weight coefficient in the random walk process is adjusted, and the risk factors include location ventilation, contact duration, personnel density and behavior habit;finally, point embedding and risk assessment are carried out to assess the importance of nodes and predict high-risk individuals and locations.Compared with the traditional network evaluation method, the present application improves the accuracy of risk prediction.
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Description

Technical Field

[0001] The present disclosure relates to the field of computers, and more particularly, to a method for enhancing epidemic prevention and management of infectious diseases through network modeling. Background Art

[0002] During an epidemic outbreak, accurately and promptly tracking and predicting the transmission paths of infectious diseases is crucial for controlling the spread of the virus. However, traditional approaches to infectious disease prevention and control have significant limitations, primarily reflected in the following aspects. First, traditional contact tracing methods typically rely on manual recording and analysis of direct contact relationships. While these methods have played a role in early infectious disease prevention and control, they are insufficient when faced with complex infectious disease transmission networks. When multiple indirect contacts or transmission across different locations are involved, simple contact tracing fails to capture potential transmission chains and high-risk individuals. This approach often overlooks the impact of complex multidimensional interactions and environmental factors on viral transmission, leading to delayed responses and inappropriate resource allocation. During the spread of infectious diseases, environmental factors such as ventilation, population density, and duration of contact have a significant impact on the risk of viral transmission. For example, the risk of viral transmission in closed indoor environments is significantly higher than in well-ventilated outdoor environments. Furthermore, individual behavior (such as whether or not to wear a mask or maintain social distance) also directly affects the probability of viral transmission. Traditional approaches to infectious disease prevention and control struggle to systematically integrate and analyze these environmental factors, resulting in significant bias in risk assessment and prediction. Modern epidemiological research and infectious disease prevention and control require more complex network analysis methods to comprehensively capture and simulate the dynamic process of infectious disease transmission. Summary of the Invention

[0003] The purpose of the embodiments of the present disclosure is to provide a method for enhancing infectious disease prevention and control through network modeling. In the early stages of an epidemic, it is crucial to promptly identify individuals who are more susceptible to infection. Therefore, in order to identify individuals who are more susceptible to infection in the early stages of an infectious disease, a new meta-path-based embedding method is proposed. By constructing a heterogeneous graph containing detailed epidemic contact element information, nodes that should be controlled earlier are predicted.

[0004] In a general aspect, a method for enhancing epidemic prevention and management of infectious diseases through network modeling is provided, which includes four processes:

[0005] First, we construct an epidemic association graph based on detailed epidemic contact information recorded in the epidemiological investigation report. The graph is a heterogeneous graph that includes infected individuals, susceptible individuals, and locations as nodes, and contacts between infected individuals, contacts between infected individuals and susceptible individuals, contacts between susceptible individuals, and relationships between infected individuals and locations as edges.

[0006] Then, by defining meta-paths, random walks are used to generate node sequences in heterogeneous graphs, capturing the semantic and structural correlations between various nodes in the heterogeneous graphs.

[0007] Then, risk factors were introduced and adjusted. That is, the weight coefficients in the random walk process were adjusted according to the risk factor levels provided by the Centers for Disease Control and Prevention. The risk factors included ventilation conditions, contact time, density of people, and behavioral habits.

[0008] Finally, point embedding and risk assessment are performed. The generated meta-path sequence is trained using the word2vec model to obtain the low-dimensional embedding vectors of the nodes. The risk factors are combined to perform risk assessment of nodes and locations. By calculating the cosine similarity between the low-dimensional embedding vectors of the nodes, the importance of the nodes is evaluated and high-risk individuals and locations are predicted.

[0009] The node must be uniquely coded.

[0010] The specific method of obtaining the low-dimensional embedding vector of the node is: given a network G = (V, E), the goal is to maximize the network probability based on the local structure, that is:

[0011]

[0012] where N(v) is the neighborhood of node v in the network G, and p(c|v;θ) defines the conditional probability of having a context node c given node v;

[0013] In heterogeneous graphs, the node embedding method is used to maximize the heterogeneous context N when a given node v is given. t (v), where t∈T represents the probability of the node type, enabling skip-gram to learn effective node representations in heterogeneous networks:

[0014]

[0015] Among them, N t (v) represents the neighborhood of the t-th type node of node v, p(c t |v;θ) is usually defined as the softmax function, that is:

[0016]

[0017] Among them, x v is the embedding vector of node v;

[0018] Random walks are applied to heterogeneous networks to generate paths of multiple types of nodes, and meta-path-based random walks are designed to generate paths that can capture the semantic and structural correlations between different types of nodes, thereby facilitating the conversion of heterogeneous network structures into skip-grams of metapath2vec.

[0019] Random walk of the metapath Defined as:

[0020]

[0021] in For node types V1 and V L The composite relationship between them, according to the defined meta-path, guides the random walk as follows:

[0022]

[0023] in, and Representation node V t+1 When the neighbor type does not match the currently defined meta-path, the wandering probability is 0, and γ is the correction coefficient affected by the epidemic risk factor.

[0024] The specific process of performing point embedding and risk assessment is as follows: using the word2vec model to train the meta-path sequence to obtain the embedding vector of the node;

[0025] Then calculate the cosine similarity between nodes:

[0026]

[0027] Where x and y are the embedding vectors of the two nodes;

[0028] By identifying the most similar nodes for each node and analyzing their importance in the network, high-risk individuals can be screened;

[0029] Combining node embedding and cosine similarity to evaluate and predict high-risk locations, a risk location dataset was constructed to count the number of connections between each location and infected individuals and rank them;

[0030] Specifically:

[0031] First, the importance of infected people is ranked according to the risk population results predicted by the model. The top k infected people are selected, and a weight is assigned to each infected person according to their ranking. The higher the ranking, the higher the weight, which means the greater the risk.

[0032] Second, we traverse each infected person and accumulate the weights of the location nodes they are connected to to obtain a score for each location. We then sort the locations based on the scores to obtain the high-risk locations with the highest assessment values.

[0033] Finally, the list of risk locations given by the model is compared with known risk locations, and the hit rate is calculated to evaluate the model performance.

[0034] The innovation of the embodiment of the present invention lies in:

[0035] This paper introduces detailed contact factor information to construct a heterogeneous graph to more accurately analyze and predict the spread of infectious diseases. It also records the basic information of infected individuals, the time of symptom onset or positive test, the specific date and time of the contact event, the location, duration of stay, and the number of contacts. In addition, factors such as whether the infected person's behavior is conducive to virus transmission, whether they wear masks, whether they use public supplies and facilities, the type of venue, the ventilation conditions of the venue, and whether the contacts wear masks properly are considered. This method proposes a risk population identification method based on network modeling, constructing a heterogeneous graph with rich semantics and diverse nodes. While obtaining risk populations, it also reflects the impact of different venues on the spread of the epidemic, thereby improving the representation of rich nodes.

[0036] This approach has the following advantages:

[0037] The use of meta-path-based random walk and node embedding technology enables the evaluation model to capture complex network structures and subtle relationships between nodes, improving the accuracy of risk prediction compared to traditional network evaluation methods.

[0038] Heterogeneous graph models, by introducing multiple types of nodes and edges, more comprehensively reflect the complexity of epidemic spread. Compared to traditional single-contact tracing methods, our approach can capture multiple relationships (such as direct and indirect contacts) between different types of nodes (such as infected individuals, susceptible individuals, and locations), thereby providing a more comprehensive risk assessment.

[0039] By identifying high-risk individuals and locations, the method of the present invention can return a risk ranking, so that in actual application, resource allocation can be optimized, and high-risk groups and key locations can be protected first, thereby improving the efficiency of epidemic prevention and control. Especially in the case of limited medical resources, the application of this method can significantly improve the prevention and control effect and reduce unnecessary waste of resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The above and other objects and features of the present disclosure will become more apparent from the following description in conjunction with the accompanying drawings.

[0041] Figure 1 2 is a schematic diagram showing a design framework of an epidemic risk management method according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0042] The following detailed description is presented to aid the reader in gaining a thorough understanding of the methods, devices, and / or systems described herein. However, various changes, modifications, and equivalents can be used, and the

[0043] The terminology used herein is for the purpose of describing particular examples only and is not intended to be limiting of the examples described herein. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0044] As used herein, the term "and / or" includes any one of the associated listed items, as well as any combination of any two or more of the associated listed items.

[0045] Although the terms "first", "second", and "third" can be used herein to describe various elements, components, regions, layers and / or sections, these elements, components, regions, layers and / or sections should not be limited by these terms. Rather, these terms are only used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, a first element, component, region, layer or section referred to herein as such can also be termed a second element, component, region, layer or section, without departing from the teachings of the examples.

[0046] In the description, when an element (such as a layer, region, or substrate) is referred to as being "on" another element, "connected to" or "coupled to" another element, it can be directly on, directly connected to, or directly coupled to the other element, or one or more other elements can be interposed therebetween. In contrast, when an element is referred to as being "directly on", "directly connected to", or "directly coupled to" another element, there are no other elements interposed therebetween.

[0047] The terminology used herein is for the purpose of describing various examples only and is not intended to be limiting of the disclosure. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," "includes," "including" and "has," "having" as used herein, specify the presence of stated features, numbers, operations, components, elements, and / or combinations thereof, but do not preclude the presence or addition of one or more other features, numbers, operations, components, elements, and / or combinations thereof.

[0048] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs when read in light of the present disclosure. Unless otherwise explicitly defined herein, the terms (such as those defined in commonly used dictionaries) should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the disclosure, and should not be interpreted in an idealized or overly formal sense.

[0049] Further, in the description of the examples, detailed descriptions of well-known related structures or functions are omitted when it is deemed that such detailed description will cause ambiguous interpretation of the present disclosure.

[0050] Figure 1 is a schematic diagram showing a method for modeling and enhancing epidemic prevention and management through a network according to an embodiment of the present disclosure.

[0051] The application is based on the way of heterogeneous graph and random walk, proposes to construct a heterogeneous graph using detailed epidemic contact information, generate a meta-path sequence through random walk, and finally realize the prediction of high-risk individuals and places through node embedding and risk factor analysis, achieve the effect of epidemic transmission risk assessment, realize the design purpose and application target.

[0052] The algorithm design process of the present application is as shown in Figure 1 First, detailed epidemic contact information is recorded according to the flow report, and an epidemic correlation graph is constructed. Then, by defining a meta-path, a node sequence in the heterogeneous graph is generated using random walk. Next, the word2vec model is used to train the generated meta-path sequence to obtain the low-dimensional embedding vector of the node. Finally, the risk factors are combined to assess the risk of nodes and places, and the high-risk individuals and places are predicted by calculating the cosine similarity between the node embedding vectors. Through this series of processes, comprehensive and accurate epidemic transmission risk assessment can be performed.

[0053] The method includes the following four parts and processes:

[0054] Epidemic correlation graph construction: Record detailed epidemic contact information and construct a heterogeneous graph containing multiple nodes (infected, susceptible, and location) and multiple edges (contact relationships). Node types include infected, susceptible, and location, and edge types include contact between infected, contact between infected and susceptible, contact between susceptible, and relationship between infected and location.

[0055] Random walk construction of meta-path sequence: Based on the defined meta-path, use random walk method to generate node sequence in heterogeneous graph. Meta-path captures the semantic and structural correlation between multiple nodes in heterogeneous graph by defining the relationship between different node types.

[0056] Introduction and adjustment of risk factors: According to the risk factor level provided by the Centers for Disease Control and Prevention (CDC), adjust the weight coefficient in the random walk process. Risk factors include location ventilation, contact duration, personnel density, and behavior habits to more accurately reflect the actual epidemic transmission risk.

[0057] Node embedding and risk assessment: Use the word2vec model to train the generated meta-path sequence to obtain the low-dimensional embedding vector of the node. By calculating the cosine similarity between node embedding vectors, the importance of the node is evaluated, and high-risk individuals and locations are predicted.

[0058] In addition, in order to train and deploy the model, it is necessary to build a running environment on the machine including pytorch and other necessary dependent libraries.

[0059] Epidemic correlation graph construction:

[0060] In the graph construction process, we assign specific attributes and labels to each node and edge to accurately reflect their roles and relationships in the epidemic transmission. The specific steps are as follows:

[0061] Node type: Node types include Susceptible, Person, Location, etc. Each node type has unique attributes, such as the health status of infected, mask wearing, social relationships of ordinary people, types of locations, ventilation, etc.

[0062] Edge type: edge type includes the contact between the infected (Susceptible-Susceptible), the contact between the infected and the susceptible (Susceptible-Person), the contact between the susceptible and the susceptible (Person-Person), the relationship between the infected and the place (Susceptible-location), the relationship between the infected and the place (Person-location), etc. The attributes of the edge include the contact time, the contact place, the contact duration and the various contact elements mentioned above.

[0063] In order to facilitate subsequent feature extraction and prevent sensitive information leakage, the nodes are uniquely coded, and after processing the complex connection relationship in the heterogeneous graph, the attribute information of each node and edge is embedded into the graph structure.

[0064] Random walk constructs epidemic correlation meta-path sequence:

[0065] The node embedding is completed by analogy to the framework of word2vec model. In word2vec, given a text corpus, the words and context concepts in the text corpus are mapped to the network. We use random walk to achieve the goal of node corpus, and use skip-gram model to learn the representation of nodes, which can promote the prediction of the structural context, i.e. local neighborhood, in the homogeneous network. Generally, given a network G=(V,E), the goal is to maximize the network probability based on the local structure, that is:

[0066]

[0067] Where N(v) is the neighborhood of node v in network G, which can be defined in different ways, such as the direct neighbor of v; and p(c|v;θ) defines the conditional probability of having context node c given node v.

[0068] And in the heterogeneous graph, the method of node embedding is used to maximize the probability of having heterogeneous context N t (v) given node v, where t∈T represents the type of node, so that skip-gram can learn effective node representation in heterogeneous network.

[0069]

[0070] Where N t (v) represents the neighborhood of the t-th type node of node v, and p(c t |v;θ) is usually defined as a softmax function, that is:

[0071]

[0072] where x v is the embedding vector of node v.

[0073] We apply random walk to the heterogeneous network to generate paths of multiple types of nodes. We design meta-path based random walk to generate paths that can capture the semantic and structural correlation between different types of nodes, thus facilitating the conversion of the heterogeneous network structure into the skip-gram of metapath2vec. Formally, the meta-path scheme is defined as the following path:

[0074]

[0075] where defines the composite relationship between node types V1and V L . For example, in the epidemic risk association graph, the meta-path "P1L1P2" represents that a susceptible person (P1) and a susceptible person (P2) have both been to a place (L1), and "S1L1P1L2P2" represents that an infected person (S1) contacts a susceptible person (P1) through a place (L1), and the susceptible person (P1) has a contact relationship with another susceptible person (P2) through a place (L2). It should be noted that in the meta-path definition, only two types of nodes P and L are involved, and the infected person S is derived together with the set of infected persons through the P node.

[0076] The way of guiding random walk according to the defined meta-path is shown in the formula

[0077]

[0078] where, and represent the neighbors of node of V t+1 type. When the neighbor type does not match the currently defined meta-path, the walk probability is 0. γ is a correction coefficient affected by the epidemic risk factor, that is, various contact elements, and the coefficient is determined according to the risk factor level provided by the CDC (Center for Disease Control and Prevention).

[0079] Point embedding and risk assessment:

[0080] After generating a series of meta-path sequences, these sequences are trained using the word2vec model to obtain the embedding vectors of the nodes. By using the node sequence generated by random walk as the input of word2vec, a low-dimensional vector representation of each node can be learned. This representation not only retains the structural information of the node, but also captures the semantic relationship between nodes. After obtaining the node embedding vector, the cosine similarity between nodes can be calculated to evaluate the importance of the node and predict high-risk populations and locations. Specifically, we measure the similarity between nodes by calculating the cosine similarity between node vectors. Cosine similarity is defined as follows:

[0081]

[0082] Where (x) and (y) are the embedding vectors of the two nodes. By calculating the cosine similarity matrix, the most similar node to each node can be identified, so as to further analyze its importance in the network. Intuitively speaking, the susceptible person who is most similar to the infected person in the feature space is also more likely to be infected, that is, the risk of infection when the two are in close contact or in contact is high, and they should be given priority control. The evaluation indicator is the hit rate, that is, how many of the predicted risk personnel are confirmed to be infected in the future. For example, in the epidemic risk association graph constructed at time T, there are three types of nodes in the graph, infected person S, susceptible person P and location L, but in fact the susceptible person can be further subdivided into infected person S at time T+t. T+t and susceptible individuals P T+t We hope that the model can predict the number of infected people S in the future as much as possible. T+t , so the predicted risk groups R and S T+t The hit rate is calculated to evaluate the model performance. Specifically, the model embeds the vector x of the infected node S according to the learning S , all remaining susceptible node vectors x can be calculated P with x s The cosine similarity of the infected nodes is then sorted by the degree of similarity to obtain the susceptible nodes {P1, P2, ...} that are most relevant to the infected node. Based on the sorting results, the risk score of the susceptible nodes with respect to the infected node S can be scored. The higher the score, the higher the score. The final risk score of the susceptible node is obtained by summing the scores of all infected nodes. The final predicted risk population R is obtained by sorting the scores and then comparing it with the actual future infected population S. T+t Compare and calculate the hit rate. The formula is as follows: T+t The ratio of the number of people in to the total number of people in R:

[0083]

[0084] Furthermore, combining node embeddings and cosine similarity can also assess and predict high-risk locations. We constructed a dataset of risky locations by counting the number of connections between each location and infected individuals (including those who may become infected in the future) and ranking them. Specifically, the number of infected individuals who visited each location was used to score the location's risk, with higher scores considered higher risk.

[0085] The specific scoring process of the location risk value of the risk prediction algorithm is as follows:

[0086] 1. Rank the importance of infected individuals based on the risk population predicted by the model, select the top k infected individuals, and assign a weight to each infected individual based on their ranking. The higher the ranking, the higher the weight, which means the greater the risk considered by the model.

[0087] 2. Traverse each infected person and accumulate the weights of the location nodes connected to them to obtain a score for each location. Sort the locations by score to obtain the high-risk locations with the highest assessment value.

[0088] 3. Compare the list of risk locations given by the model with known risk locations and calculate the hit rate to evaluate model performance.

[0089] Specifically, similar to the calculation method of risk population, the model embeds the vector x according to the learned infected node S S , all remaining location node vectors x can be calculated L with x s The cosine similarity of the locations is then sorted by similarity to obtain the most relevant location nodes {L1, L2, …} for the infected node. Based on the sorting results, the risk of the location nodes with respect to infected person S is scored, with the higher the score, the higher the score. The final risk score for the location is then calculated by summing the scores for all infected locations. The final predicted risk location C is then compared with the list Q of locations with the highest number of actual infected people, and the hit rate is calculated using the following formula: the ratio of the number of people in C who correctly appear in Q to the total number of locations in C:

[0090]

[0091] While some embodiments of the present disclosure have been shown and described, it will be appreciated by those skilled in the art that changes may be made to these embodiments without departing from the principles and spirit of the disclosure, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for enhancing epidemic prevention and management of infectious diseases through network modeling, characterized in that: It includes four processes: First, we construct an epidemic association graph based on detailed epidemic contact information recorded in the epidemiological investigation report. The graph is a heterogeneous graph that includes infected individuals, susceptible individuals, and locations as nodes, and contacts between infected individuals, contacts between infected individuals and susceptible individuals, contacts between susceptible individuals, and relationships between infected individuals and locations as edges. Then, by defining meta-paths, random walks are used to generate node sequences in heterogeneous graphs, capturing the semantic and structural correlations between various nodes in the heterogeneous graphs. Then, risk factors were introduced and adjusted. That is, the weight coefficients in the random walk process were adjusted according to the risk factor levels provided by the Centers for Disease Control and Prevention. The risk factors included ventilation conditions, contact time, density of people, and behavioral habits. Finally, we perform point embedding and risk assessment. We use the word2vec model to train the generated meta-path sequence to obtain low-dimensional embedding vectors for the nodes. We then combine risk factors to perform risk assessment for nodes and locations. By calculating the cosine similarity between the low-dimensional embedding vectors of the nodes, we assess the importance of the nodes and predict high-risk individuals and locations. The specific method of obtaining the low-dimensional embedding vector of the node is: given a network ,The goal is to maximize the network probability based on the local structure,,that is: in, It's the network midpoint Neighborhood, Defines the The case has a context node The conditional probability of In heterogeneous graphs, the node embedding method is used to maximize the Heterogeneous context ,in Representing the probability of node types enables skip-gram to learn effective node representations in heterogeneous networks: in, Representation node No. Neighborhood of type node, It is usually defined as the softmax function, that is: in, is a node Embedding vector of Random walks are applied to heterogeneous networks to generate paths of multiple types of nodes, and meta-path-based random walks are designed to generate paths that can capture the semantic and structural correlations between different types of nodes, thereby facilitating the conversion of heterogeneous network structures into skip-grams of metapath2vec.

2. The method for enhancing epidemic prevention and management of infectious diseases through network modeling according to claim 1, characterized in that: The node must be uniquely coded.

3. The method for enhancing epidemic prevention and management of infectious diseases through network modeling according to claim 1, characterized in that: Random walk of the metapath Defined as: in , is the node type and The composite relationship between them, according to the defined meta-path, guides the random walk as follows: in, and Representation node of When the neighbor type does not match the currently defined meta-path, the wandering probability is 0. is the correction coefficient affected by epidemic risk factors.

4. The method for enhancing epidemic prevention and management of infectious diseases through network modeling according to claim 1, characterized in that: The specific process of performing point embedding and risk assessment is as follows: using the word2vec model to train the meta-path sequence to obtain the embedding vector of the node; Then calculate the cosine similarity between nodes: Where x and y are the embedding vectors of the two nodes; By identifying the most similar nodes for each node and analyzing their importance in the network, high-risk individuals can be screened; Combining node embedding and cosine similarity to evaluate and predict high-risk locations, a risk location dataset was constructed to count the number of connections between each location and infected individuals and rank them; Specifically: First, the importance of infected people is ranked according to the risk population predicted by the model. The top k infected people are selected and a weight is assigned to each infected person based on their ranking. The higher the ranking, the higher the weight, which means the greater the risk. Second, we traverse each infected person and accumulate the weights of the location nodes they are connected to to obtain a score for each location. We then sort the locations based on the scores to obtain the high-risk locations with the highest assessment values. Finally, the list of risk locations given by the model is compared with known risk locations, and the hit rate is calculated to evaluate the model performance.

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