Dynamic Intervention Methods and Systems for Key Nodes of Epidemic Transmission in Three-Dimensional Space

Abstract

This invention relates to a dynamic intervention method for key nodes in a three-dimensional space epidemic transmission hypernetwork, comprising: modeling the transmission process in the three-dimensional space as a two-layer network including an information space layer and a physical space layer, defining the node state transition probabilities and cross-layer coupling mechanisms within each layer; modeling the intervention task as a dynamic key node control problem under budget constraints, establishing a finite-time-domain Markov decision process framework, with minimizing the cumulative number of infections as the optimization objective; constructing node feature vectors that integrate topological statistical features and single-hot encoding of node states, extracting node embeddings from the information space layer and the physical space layer respectively, and generating a three-dimensional space state-aware node representation matrix; and ensuring the legality of actions through masked Softmax, improving training stability and policy generalization ability. This invention also relates to a dynamic intervention system for key nodes in a three-dimensional space epidemic transmission hypernetwork. This invention enables adaptive and accurate identification and intervention of key nodes in the three-dimensional space under dynamic, finite-budget constraints.

Description

Technical Field

[0001] This invention relates to the fields of complex network control and public health emergency management, and in particular to a dynamic intervention method and system for key nodes of a three-dimensional spatial epidemic transmission hypernetwork. Background Technology

[0002] With the deep penetration of information technology, human society has formed a highly integrated Cyber-Physical-Social Space (CPSS), which comprises cyberspace, physical space, and social space. In this CPSS, individuals exist simultaneously in online information networks and offline physical contact networks, forming a close structural coupling and behavioral feedback loop among the three.

[0003] Major public health events have profoundly revealed the core role of the three-dimensional space in the spread of infectious diseases: viruses spread through contact networks in the physical space, while a large number of epidemic-related rumors spread rapidly on social media platforms (Facebook, TikTok, etc.) in the information space. Furthermore, cognitive biases and behavioral changes (such as ignoring protective measures) arising from these rumors in the social space, in turn, accelerate the spread of the epidemic in the physical space. The World Health Organization refers to this complex phenomenon of rumors and the epidemic spreading synergistically in the three-dimensional space as an "infodemic." Therefore, effective epidemic prevention and control must model and intervene in the spread of rumors in the information space and the spread of disease in the physical space as a unified three-dimensional coupled system.

[0004] However, given the limited resources available, such as vaccine reserves, medical resources, and administrative budgets, implementing universal interventions for the entire population is often impractical. Identifying and prioritizing interventions for key individuals within the three-dimensional space (super-spreaders of rumors in the information space or core infection hubs in the physical space) under resource constraints, in order to cut off cross-space transmission paths and minimize the cumulative scale of infections at the lowest cost, has become a core challenge for network science and public health governance.

[0005] Existing intervention methods can be broadly classified into two categories: The first category is heuristics based on centrality measures, including degree centrality, betweenness centrality, and... k - Kernel decomposition, eigenvector centrality, and PageRank, as well as multi-path PageRank, tensor centrality, and cross-layer aggregation for multi-layer networks. kExtended metrics such as kernel decomposition and coupling-sensitive centrality designed specifically for rumor-pandemic coupling scenarios. However, these methods essentially produce static rankings or approximate dynamic sortings that rely on weak update rules. They fail to capture the time-varying criticality of nodes in the co-evolution of the ternary space, driven by both topological changes and real-time state updates (such as the rumor propagation state in the information space and the infection state in the physical space). Consequently, they often produce suboptimal intervention effects in highly dynamic and feedback-driven co-evolution scenarios.

[0006] The second category is data-driven methods that combine Graph Neural Networks (GNNs) with Deep Reinforcement Learning (DRL). These methods learn optimal sequence policies by simultaneously capturing topological and dynamic state information, and have achieved encouraging results in single-layer (single-space) dynamic scenarios such as opinion control and vaccine priority allocation. However, existing GNN-DRL methods mainly rely on single-layer propagation dynamics, making it difficult to model the instantaneous feedback mechanisms generated by multi-layer coupling between the information space and physical space. They also lack mechanisms specifically for handling state space explosion and cross-space dependencies in the co-evolution of ternary spaces, and cannot capture the amplification effect of rumor-driven behavioral changes in the information space on the spread of the epidemic in the physical space, or the accelerating effect of the infection status in the physical space on the annihilation of rumors in the information space. Summary of the Invention

[0007] In view of this, it is necessary to provide a dynamic intervention method and system for key nodes of the three-dimensional space epidemic transmission supernetwork, which can solve the problems that existing technologies cannot perceive the dynamic of cross-layer collaborative evolution in the three-dimensional space and are difficult to achieve precise intervention driven by cross-space feedback under limited budget.

[0008] This invention provides a dynamic intervention method for key nodes in a three-dimensional space epidemic transmission hypernetwork. The method includes: Step S1, modeling the collaborative propagation process of rumors and epidemics in the information-physical-social three-dimensional space as a two-layer network: the rumor propagation network in the information space composed of social media platforms as the rumor layer, and the disease transmission network in the physical space composed of physical contact networks as the epidemic layer; embedding the node set into two undirected graphs with different topologies simultaneously, defining the state transition probability and cross-layer coupling mechanism of each node in the two layers respectively, to characterize the bidirectional dynamic feedback formed between the information space and physical space through individual behavior in the social space; Step S2, formalizing the intervention task as a dynamic key node control problem under budget constraints, establishing a finite-time domain Markov decision process framework to minimize the cumulative number of infections within the control time domain. To optimize the objective, one node is selected from the active node set for isolation at each step until the global budget is exhausted. In step S3, a node feature vector containing topological statistical features and single-hot encoding of node states is constructed. The node embeddings of the rumor layer and the epidemic layer are extracted using an intra-layer multi-head graph attention network with independent parameters. Then, the two layers of embeddings are integrated into a state-aware node representation matrix through an adaptive cross-layer attention fusion mechanism. In step S4, a sequence intervention strategy is trained based on a near-end policy optimization algorithm. The masked softmax ensures that only legal actions are sampled from the active node set at each step. An adaptive course learning strategy is adopted to gradually increase the complexity of the training task in the order of increasing network size and increasing topology from homogeneous to heterogeneous. Knowledge transfer is achieved through cross-stage parameter inheritance to improve the stability of policy training and cross-scale generalization ability.

[0009] Step S1 includes: The ternary spatial propagation structure is formalized as a two-layer network: Let the set of nodes be... V = {1 , . . . ,N This is then embedded into two undirected graphs with different topologies—corresponding to the rumor layer in the information space. and the corresponding physical space epidemic layer The two layers share the same set of nodes but have their own independent set of edges; The node state space of the rumor layer is defined as follows: , respectively representing the unknown, the rumor spreader, and the destroyer; the node state space of the epidemic layer is defined as S (e) = { S, I,R These correspond to the classic states of susceptibility, infection, and recovery, respectively; at any given moment... t ,node i The two-level state is denoted as: (1).

[0010] Step S1 further includes: Nodes update their own state based on the state of their neighbors within each layer, propagating parameters along the baseline. β r γ r and β e γ e Based on this, the intra-layer baseline state transition probability is defined as:

[0011] (2)

[0012] (3) in Represents a node i In the neighbor set of the corresponding layer, 1[ · ] is an indicator function; Cross-layer coupling is achieved by modulating state transition probabilities at the node level, as follows:

[0013] (4) in α 1 ≥ 0 represents the susceptibility amplification factor caused by the spread of rumors. α 2 ≥ 0 represents the annihilation rate enhancement factor caused by the infected state; both are set to bounded values ​​to ensure that the modulated probability value is within (0 ≤ ... , 1) Within the scope; Substituting the above equation into the baseline transition rule, we obtain the final coupled state transition probability: (5) .

[0014] Step S2 includes: set up For a moment t layer ∈ { r, e The active network topology, with the controller at each step starting from the set of active nodes. V t Select action a t ∈ V t The target node is isolated, and its influence in both layers is cut off. The network topology update rule is as follows:

[0015] (6) The isolated node no longer participates in any neighbor-driven propagation or transfer, but its state is still continuously tracked for evaluation; Defining the prevalence of an epidemic For a moment t In the original node set V The above statistics show the number of infections; the optimal intervention strategy a = { a 0 , a 1 , . . . , a T The objective of solving 1} is: (7) The constraints are , ;exist T = B Under this setting, each step isolates exactly one node, and the budget constraint is automatically satisfied by the constructor.

[0016] Step S2 further includes: The above problem can be modeled as a finite-time Markov decision process: state: S t = (Z t , b t ),in This is the state-aware embedding matrix for each active node at the current moment. b t = B t Provide the strategy with a clear, limited temporal awareness of the remaining intervention steps; action: a t ∈ V t That is, select one node from the set of active nodes to perform isolation; award: R t = N I ( t + 1), maximizing the cumulative reward is directly aligned with minimizing the infection in the objective function (7); State transition: during the execution of an action a t Afterwards, the network topology is updated according to equation (6), and then the rumors and epidemic dynamics propagate on the updated topology according to equations (2)–(5), generating new node states to construct the state for the next time step. St+1 .

[0017] Step S3 includes: The CLA encoder transforms the heterogeneous structure and interdependencies of a two-layer network into a high-level state-aware node representation through three stages: (1) Construction of node features For time t Each node i Construct the input feature vector: (8) in and These are the structural features (including topological statistics such as degree and centrality) calculated on the current active topologies of the epidemic layer and the rumor layer, respectively; i ( t This refers to the one-hot encoding concatenation of the node's two-layer state: (9) This construction ensures a two-layer state space. S ( r ) × S ( e The semantics of ) are preserved and effectively utilized; (2) In-layer multi-head graph attention network Two parallel multi-head graph attention networks (GAT) are used to focus on the epidemic layer. and rumor layer Extract the structural patterns within the layers, and maintain independent parameters for each layer to preserve semantic distinction; Node embeddings are initialized via learnable linear projections: (10) node i In the layer No. l The feature update rule for layer +1 is: (11) in H For the number of attention heads, To quantify neighbor nodes j For nodes i Attention coefficient of importance; L After layer graph attention, the final embeddings of each layer are obtained. and The corresponding layer feature matrix H (e) ( t ) and H (r) ( t ); (3) Adaptive cross-layer attention fusion To capture the heterogeneity of node roles across different layers, an adaptive gating mechanism is introduced to dynamically fuse the two decoupled representations: First, concatenate the two embedded layers and compute the soft-gating attention weights: (12) in, Soft gating weights are used to control information flow at each layer; Then, the weighted fusion embedding is calculated: (13) Finally, the final state-aware node representation is obtained through nonlinear refinement: (14) The final output node representation matrix It provides a high-level, real-time state-aware representation of the cooperative evolution network for reinforcement learning agents.

[0018] Step S4 includes: Based on the node representation matrix Z generated in step S3 t The Actor network computes the logit value of each node by sharing an MLP: (15) in g θ ( · This is a shared MLP applied node-by-node; to ensure sampling of valid actions, a binary mask m is defined. t :when i ∈ V t hour m i ( t ) = 1, otherwise m i ( t ) = 0; Action probability is calculated using a mask Softmax: (16) The Critic network first embeds variable-length nodes into matrix Z. t The representation is compressed into a fixed-dimensional graph level by permutation-invariant mean / sum pooling, and then the output state value is estimated by a lightweight MLP. V ψ ( S t ), used for PPO updates.

[0019] Step S4 further includes: To address the state space explosion problem in large-scale heterogeneous networks, a course learning strategy is introduced, dividing the training process into... K Each stage k ∈ {1 , . . . ,K} Corresponding task tuple M (k) = ( N (k) , T (k) , Θ (k) ), specify the network size, topology type, and propagation dynamics parameters respectively; The course difficulty increases progressively along two main dimensions: (1) Increasing scale: N (1) <N (2) <· · ·<N (K) This guides intelligent agents to gradually adapt to large-scale networks from small-scale networks. (2) Structural heterogeneity: topological type T (k) The model evolves from random homogeneous networks to structurally heterogeneous networks with high clustering coefficients or heavy-tailed distributions, allowing it to first master basic dynamic operators in symmetric networks and then transition to complex topologies where structural heterogeneity has a nonlinear impact on the co-evolution of rumors and the pandemic.

[0020] This invention provides a dynamic intervention system for key nodes in a three-dimensional spatial epidemic transmission supernetwork. The system includes a co-evolutionary modeling module, a decision-making process framework establishment module, a cross-layer attention encoding module, and an intervention strategy training module, wherein: The co-evolution modeling module is used to model the collaborative propagation process of rumors and epidemics in the information-physical-social ternary space as a two-layer network: the rumor propagation network in the information space composed of social media platforms is the rumor layer, and the disease propagation network in the physical space composed of physical contact networks is the epidemic layer; the node set is embedded into two undirected graphs with different topological structures at the same time, and the state transition probability and cross-layer coupling mechanism of each node in the two layers are defined respectively to characterize the two-way dynamic feedback between the information space and the physical space through individual behavior in the social space; The decision process framework establishment module is used to formalize the intervention task into a dynamic key node control problem under budget constraints, establish a finite time domain Markov decision process framework, take minimizing the cumulative number of infected people in the control time domain as the optimization objective, and select one node from the active node set for isolation in each step until the global budget is exhausted. The cross-layer attention encoding module is used to construct a node feature vector that includes topological statistical features and node state one-hot encoding. It uses an intra-layer multi-head graph attention network with independent parameters to extract node embeddings from the rumor layer and the epidemic layer respectively. Then, it integrates the two layers of embeddings into a state-aware node representation matrix through an adaptive cross-layer attention fusion mechanism. The intervention strategy training module is used to train sequence intervention strategies based on the near-end policy optimization algorithm. It ensures that each step only samples legal actions from the active node set through mask Softmax. It also adopts an adaptive course learning strategy, which gradually increases the complexity of the training task in the order of increasing network size and increasing topology from homogeneous to heterogeneous. Knowledge transfer is achieved through cross-stage parameter inheritance, thereby improving the stability of policy training and cross-scale generalization ability.

[0021] The beneficial effects of this application include: (1) Unified dynamic intervention framework for the three-dimensional space: This invention explicitly models the rumor-epidemic collaborative propagation process in the information-physical-social three-dimensional space as a two-layer structure coupled with the information space layer (rumor propagation network) and the physical space layer (disease contact network), and models the intervention as a dynamic, budget-constrained sequence node isolation problem. This provides a unified framework for studying the cross-space coupling propagation process in the three-dimensional space, and makes up for the limitations of existing methods that ignore the structural coupling between the information space and the physical space and make a single static selection on a fixed multi-layer topology.

[0022] (2) Cross-layer feedback perception node representation: The CLA encoder integrates the structural and dynamic state information of the rumor layer and the epidemic layer into a real-time state perception node representation through intra-layer multi-head graph attention aggregation and adaptive cross-layer attention fusion. This enables the reinforcement learning agent to perceive non-stationary environments in the evolutionary network, accurately identify and prioritize interventions on key nodes under strict budget constraints, and significantly improve the accuracy and timeliness of interventions.

[0023] (3) Curriculum-driven stable training and cross-scale generalization: The adaptive curriculum learning mechanism counteracts the non-stationarity of the system through progressive difficulty scaling, stabilizing the training process so that the policy trained by the curriculum can be directly deployed to networks of different scales without retraining, in synthetic networks ( N ∈ {300 , 500 , 700 , Experiments on 1000 showed that the strategy achieved optimal intervention results in 26 / 27 scale-topology combinations.

[0024] (4) Strong robustness and excellent stability: In adversarial perturbation scenarios with random rumor injection and high-number nodes as rumor sources, this method reduces the cumulative infection rate by about 14% to 18% compared with the best baseline method, and maintains the minimum cross-experimental fluctuation under all settings. Pareto optimality analysis confirms that this method is always superior to all baseline methods on the "mean infection rate - standard deviation" plane. Attached Figure Description

[0025] Figure 1 This is a flowchart of the dynamic intervention method for key nodes of the ternary spatial epidemic transmission hypernetwork of the present invention; Figure 2 This is a schematic diagram illustrating the sequence intervention process in an embodiment of the present invention; wherein, the rumor layer corresponds to the information space, and the epidemic layer corresponds to the physical space; Figure 3 This is a schematic diagram of the ternary spatial rumor-epidemic co-evolution model according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the overall structure of the ARISE framework according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the cross-spatial attention encoder (CLA encoder) structure according to an embodiment of the present invention; Figure 6 This is a hardware architecture diagram of the dynamic intervention system for key nodes of the three-dimensional space epidemic transmission supernetwork of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0027] See Figure 1 The diagram shown is a flowchart of a preferred embodiment of the dynamic intervention method for key nodes of the ternary spatial epidemic transmission hypernetwork of the present invention. Please refer to it as well. Figures 2-5 .

[0028] Step S1 involves modeling the collaborative propagation process of rumors and epidemics in the information-physical-social ternary space as a two-layer network: the rumor layer is the rumor propagation network in the information space constituted by social media platforms, and the epidemic layer is the disease transmission network in the physical space constituted by physical contact networks. The node set is simultaneously embedded into two undirected graphs with different topologies, and the state transition probabilities and cross-layer coupling mechanisms of each node within the two layers are defined to characterize the bidirectional dynamic feedback between the information space and physical space through individual behaviors in the social space. Specifically: Three-dimensional spatial two-layer network structure and node state definition: In the information-physical-social triadic space, individuals are active simultaneously in the information space (social media platforms, where rumors spread) and the physical space (offline contact networks, where diseases spread), forming a bidirectional coupling through individual cognition and behavior in the social space. This embodiment formalizes the triadic space propagation structure as a two-layer network: let the set of nodes... V = {1 , . . . ,N This is then embedded into two undirected graphs with different topologies—corresponding to the rumor layer in the information space. and the corresponding physical space epidemic layer The two layers share the same set of nodes but have their own independent set of edges.

[0029] The node state space of the rumor layer is defined as follows: , representing Unaware, Rumor Spreader, and Stifler respectively; the node state space of the epidemic layer is defined as S (e) ={ S, I,R These correspond to the classic states of Susceptible, Infected, and Recovered, respectively. At time... t ,node i The two-level state is denoted as: (1) Intra-layer state transition probability: Nodes update their own state based on the states of their neighbors within each layer. Parameters are propagated using the baseline. β r γ r (Rumor layer) and β e 、 γ e Based on the (epidemic layer), the probability of baseline state transition within the layer is defined as:

[0030] (2)

[0031] (3) in Represents a node i In the neighbor set of the corresponding layer, 1[ · ] is an indicator function.

[0032] Cross-layer coupling mechanism: Empirical studies have shown a significant two-way interaction between the spread of rumors and the spread of disease: rumor spreaders often ignore protective measures, leading to an increased probability of infection; while infected individuals are usually more sensitive to authoritative information, and their probability of stopping the spread of rumors also increases.

[0033] To quantify this bidirectional feedback, this embodiment achieves cross-layer coupling by modulating the state transition probability at the node level, as detailed below:

[0034] (4) in α 1 ≥ 0 represents the susceptibility amplification factor caused by the spread of rumors. α 2 ≥ 0 represents the annihilation rate enhancement factor caused by the infected state; both are set to bounded values ​​to ensure that the modulated probability value is within (0 ≤ ... , 1) Within the range.

[0035] Substituting the above equation into the baseline transition rule, we obtain the final coupled state transition probability: (5)

[0036] Thus, the rumor-epidemic co-evolution model fully describes the temporal evolution of the two-layer state of the nodes and the interaction feedback mechanism between the two layers.

[0037] Step S2 formalizes the intervention task as a dynamic critical node control problem under budget constraints, establishing a finite-time Markov decision process framework. The optimization objective is to minimize the cumulative number of infections within the control time domain. At each step, one node is selected from the active node set for isolation, until the global budget is exhausted. Specifically, this includes: Sequence node intervention: set up For a moment t layer ∈ { r, e The active network topology. Under a uniform cost setting, the global budget... B The total number of nodes that can be isolated within the control time domain is specified. Each step of the controller starts from the set of active nodes. V t Select action a t ∈ V t The target node is isolated. Isolation is interpreted as a comprehensive control measure (such as physical isolation combined with digital account restrictions or targeted disinformation), simultaneously cutting off the node's influence at both layers. The network topology update rules are as follows:

[0038] (6) The isolated node no longer participates in any neighbor-driven propagation transfers, but its state is still continuously tracked for evaluation.

[0039] Optimization goal: Defining the prevalence of an epidemic For a moment t In the original node set V The above statistics show the number of infections. The optimal intervention strategy a = { a 0 , a 1 , . . . , a T The objective of solving 1} is: (7) The constraints are , .exist T = B Under this setting, each step isolates exactly one node, and the budget constraint is automatically satisfied by the constructor.

[0040] Formalization of Markov decision processes: The above problem can be modeled as a finite-time Markov decision process: • state: S t = (Z t , b t ),in This is the state-aware embedding matrix for each active node at the current moment. b t = B t Provide the strategy with a clear, limited temporal awareness of the remaining intervention steps; • Action: a t ∈ V t That is, select one node from the set of active nodes to perform isolation; • award: R t = N I ( t + 1), maximizing the cumulative reward is directly aligned with minimizing the infection in the objective function (7); • State transition: during the execution of an action a tAfterwards, the network topology is updated according to equation (6), and then the rumors and epidemic dynamics propagate on the updated topology according to equations (2)–(5), generating new node states to construct the state for the next time step. S t+1 .

[0041] Step S3: Construct a node feature vector containing topological statistical features and single-hot encoding of node states. Use an intra-layer multi-head graph attention network with independent parameters to extract node embeddings from the rumor layer and the epidemic layer respectively. Then, integrate the two embeddings into a state-aware node representation matrix through an adaptive cross-layer attention fusion mechanism. Specifically: The CLA encoder transforms the heterogeneous structure and interdependencies of a two-layer network into a high-level state-aware node representation (e.g., ...) through three stages. Figure 5 (As shown).

[0042] (1) Construction of node features For time t Each node i Construct the input feature vector: (8) in and These are the structural features (including topological statistics such as degree and centrality) calculated on the current active topologies of the epidemic layer and the rumor layer, respectively; i ( t This refers to the one-hot encoding concatenation of the node's two-layer state: (9) This construction ensures a two-layer state space. S ( r ) × S ( e The semantics of ) are preserved and effectively utilized.

[0043] (2) In-layer multi-head graph attention network Two parallel multi-head graph attention networks (GAT) are used to focus on the epidemic layer. and rumor layer Extract the structural patterns within the layers, and maintain independent parameters for each layer to preserve semantic distinctions.

[0044] Node embeddings are initialized via learnable linear projections: (10) node i In the layer No. l The feature update rule for layer +1 is: (11) inH For the number of attention heads, To quantify neighbor nodes j For nodes i Attention coefficient for importance. L After layer graph attention, the final embeddings of each layer are obtained. and The corresponding layer feature matrix H (e) ( t ) and H (r) ( t ).

[0045] (3) Adaptive cross-layer attention fusion To capture the heterogeneity of node roles across different layers, an adaptive gating mechanism is introduced to dynamically fuse the two decoupled representations: First, concatenate the two embedded layers and compute the soft-gating attention weights: (12) in, Soft gating weights are used to control the information flow at each layer.

[0046] Then, the weighted fusion embedding is calculated: (13) Finally, the final state-aware node representation is obtained through nonlinear refinement: (14) The final output node representation matrix It provides a high-level, real-time state-aware representation of the cooperative evolution network for reinforcement learning agents.

[0047] Step S4 involves training a sequence intervention strategy based on a near-end policy optimization algorithm. A masked softmax method ensures that each step samples only legal actions from the active node set. An adaptive course learning strategy is employed, gradually increasing the training task complexity according to network size (from small to large) and topology (from homogeneous to heterogeneous). Knowledge transfer is achieved through cross-stage parameter inheritance, improving the stability of strategy training and its cross-scale generalization ability. Specifically: Constraint-aware policy sampling: Based on the node representation matrix Z generated in step S3 t The Actor network computes the logit value of each node by sharing an MLP: (15) in g θ ( · This is a shared MLP applied node-by-node. To ensure sampling of valid actions, a binary mask m is defined. t :wheni ∈ V t hour m i ( t ) = 1, otherwise m i ( t = 0. The action probability is calculated using a masked Softmax: (16) The Critic network first embeds variable-length nodes into matrix Z. t The representation is compressed into a fixed-dimensional graph level by permutation-invariant mean / sum pooling, and then the output state value is estimated by a lightweight MLP. V ψ ( S t ), used for PPO updates.

[0048] Adaptive learning strategies: To address the state space explosion problem in large-scale heterogeneous networks, a course learning strategy is introduced, dividing the training process into... K Each stage k ∈ {1 , . . . ,K} Corresponding task tuple M (k) = ( N (k) , T (k) , Θ (k) ), specifying the network size, topology type, and propagation dynamics parameters respectively.

[0049] The course difficulty increases progressively along two main dimensions: (1) Increasing scale: N (1) <N (2) <· · ·<N (K) This guides intelligent agents to gradually adapt to large-scale networks from small-scale networks. (2) Structural heterogeneity: topological type T (k) The model evolves from random homogeneous networks (ER diagrams) to structurally heterogeneous networks with high clustering coefficients (WS diagrams) or heavy-tailed distributions (BA diagrams), allowing the model to first master the basic dynamic operators in symmetric networks and then transition to complex topologies where structural heterogeneity has a nonlinear impact on the co-evolution of rumors and the epidemic.

[0050] Furthermore, a cross-stage parameter inheritance mechanism is employed to facilitate knowledge transfer: entering the... kIn phase +1, the Actor and Critic networks inherit the... k The final parameters of the stage, i.e. , This ensures that the graph representation capabilities learned in low-dimensional tasks are systematically transferred to higher-dimensional scenarios, significantly reducing exploration costs and enhancing the evolutionary stability of strategies in heterogeneous dynamic environments.

[0051] See Figure 6 The diagram shown is a hardware architecture diagram of the dynamic intervention system 10 for key nodes of the three-dimensional space epidemic transmission supernetwork of the present invention. The system includes: a co-evolution modeling module 101, a decision process framework establishment module 102, a cross-layer attention encoding module 103, and an intervention strategy training module 104.

[0052] The co-evolution modeling module 101 is used to model the collaborative propagation process of rumors and epidemics in the information-physical-social ternary space as a two-layer network: the rumor propagation network in the information space composed of social media platforms is the rumor layer, and the disease propagation network in the physical space composed of physical contact networks is the epidemic layer; the node set is embedded into two undirected graphs with different topological structures at the same time, and the state transition probability and cross-layer coupling mechanism of each node in the two layers are defined respectively to characterize the two-way dynamic feedback formed by the individual behavior of the social space between the information space and the physical space.

[0053] The decision process framework establishment module 102 is used to formalize the intervention task into a dynamic key node control problem under budget constraints, establish a finite time domain Markov decision process framework, take minimizing the cumulative number of infected people in the control time domain as the optimization objective, and select one node from the active node set for isolation in each step until the global budget is exhausted.

[0054] The cross-layer attention encoding module 103 is used to construct a node feature vector containing topological statistical features and node state one-hot encoding. It uses an intra-layer multi-head graph attention network with independent parameters to extract node embeddings from the rumor layer and the epidemic layer respectively, and then integrates the two layers of embeddings into a state-aware node representation matrix through an adaptive cross-layer attention fusion mechanism.

[0055] The intervention strategy training module 104 is used to train the sequence intervention strategy based on the near-end strategy optimization algorithm. It ensures that each step only samples legal actions from the active node set through the mask Softmax. It also adopts an adaptive course learning strategy, which gradually increases the complexity of the training task in the order of network size from small to large and topology from homogeneous to heterogeneous. Knowledge transfer is achieved through cross-stage parameter inheritance, thereby improving the stability of strategy training and cross-scale generalization ability.

[0056] Experimental verification: In synthetic networks ( N ∈ {300, 500 , 700 , A systematic experiment was conducted on 1000} topologies including ER-ER, ER-WS, ER-BA, WS-ER, WS-WS, WS-BA, BA-ER, BA-WS, and BA-BA (a total of 9 two-layer combinations) and 5 real-world node-aligned multilayer networks (Climate, Celegans, EuAir, Physicians, and Athletics).

[0057] Simulation parameters are set as follows: baseline propagation probability β e = β r = 0 . 01, Probability of Recovery / Annihilation γ e = γ r = 0 . 01, Cross-layer coupling parameters α 1= α 2 = 0 . 2. Intervention budget B = 50, the result is the mean of 10 independent experiments. ± Standard deviation.

[0058] Experimental results show that the present invention achieved the lowest final cumulative infection rate in all test scenarios. I cum ( T )= N cum ( T ) / N In synthetic networks ( N On (= 500), the cumulative infection rate of this invention on the ER-ER topology is 0. . 7200, compared to the best benchmark CGNN (0 . 7420) decreased by approximately 3 . 0%; drops to 0 on WS-ER topology. . 3994, compared to MultiDismantler (0 . 4482) decreased by approximately 10 . 9%. On the real-world EuAir network, this invention reduces the infection rate to 0. . 4497, compared to FINDER (0 . 5249) achieved approximately 14 . A relative increase of 3%. Ablation experiments further validated the contributions of each core module: removing the rumor layer features led to a 49% increase in infection rate. .67%, with the removal of courses leading to a 25% increase. . 22%, removal of cross-layer adaptive fusion led to an increase of 22%. . 81%.

[0059] This invention can construct a two-layer co-evolutionary structure of rumor propagation network (information space layer) and disease contact network (physical space layer) and incorporate a cross-space attention mechanism to achieve adaptive and accurate identification and intervention of key nodes in the three-dimensional space under dynamic and limited budget constraints. In other words, it can realize the intervention of dynamic key nodes in the rumor-epidemic co-evolutionary network in the three-dimensional space of information-physical-social.

[0060] Although the present invention has been described with reference to the present preferred embodiments, those skilled in the art should understand that the above preferred embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A dynamic intervention method for key nodes in a three-dimensional spatial epidemic transmission supernetwork, characterized in that, The method includes: Step S1: Model the collaborative propagation process of rumors and epidemics in the information-physical-social ternary space as a two-layer network: the rumor propagation network in the information space composed of social media platforms is the rumor layer, and the disease propagation network in the physical space composed of physical contact networks is the epidemic layer; embed the node set into two undirected graphs with different topologies at the same time, and define the state transition probability and cross-layer coupling mechanism of each node in the two layers respectively, so as to characterize the two-way dynamic feedback between the information space and the physical space through individual behavior in the social space; Step S2: The intervention task is formalized as a dynamic critical node control problem under budget constraints. A finite time-domain Markov decision process framework is established with the optimization objective of minimizing the cumulative number of infected people in the control time domain. In each step, one node is selected from the set of active nodes to implement isolation until the global budget is exhausted. Step S3: Construct a node feature vector containing topological statistical features and single-hot encoding of node states. Use an intra-layer multi-head graph attention network with independent parameters to extract node embeddings from the rumor layer and the epidemic layer respectively. Then, integrate the two layers of embeddings into a state-aware node representation matrix through an adaptive cross-layer attention fusion mechanism. Step S4: Train the sequence intervention strategy based on the near-end policy optimization algorithm. Use masked Softmax to ensure that each step only samples legal actions from the active node set. Adaptive course learning strategy is adopted to gradually increase the complexity of the training task in the order of increasing network size and increasing topology from homogeneous to heterogeneous. Knowledge transfer is achieved through cross-stage parameter inheritance to improve the stability of policy training and cross-scale generalization ability.

2. The method as described in claim 1, characterized in that, Step S1 includes: The ternary spatial propagation structure is formalized as a two-layer network: Let the set of nodes be... V = {1 , . . . ,N This is then embedded into two undirected graphs with different topologies—corresponding to the rumor layer in the information space. and the corresponding physical space epidemic layer The two layers share the same set of nodes but have their own independent set of edges; The node state space of the rumor layer is defined as follows: , respectively representing the unknown, the rumor spreader, and the destroyer; the node state space of the epidemic layer is defined as S (e) = { S, I,R These correspond to the classic states of susceptibility, infection, and recovery, respectively; at any given moment... t ,node i The two-level state is denoted as: （1）。 3. The method as described in claim 2, characterized in that, Step S1 further includes: Nodes update their own state based on the state of their neighbors within each layer, propagating parameters along the baseline. β r γ r and β e γ e Based on this, the intra-layer baseline state transition probability is defined as: （2） （3） in Represents a node i In the neighbor set of the corresponding layer, 1[ · ] is an indicator function; Cross-layer coupling is achieved by modulating state transition probabilities at the node level, as follows: （4） in α 1 ≥ 0 represents the susceptibility amplification factor caused by the spread of rumors. α 2 ≥ 0 represents the annihilation rate enhancement factor caused by the infected state; both are set to bounded values ​​to ensure that the modulated probability value is within (0 ≤ ... , 1) Within the scope; Substituting the above equation into the baseline transition rule, we obtain the final coupled state transition probability: （5） 。 4. The method as described in claim 3, characterized in that, Step S2 includes: set up For a moment t layer ∈ { r, e The active network topology, with the controller at each step starting from the set of active nodes. V t Select action a t ∈ V t The target node is isolated, and its influence in both layers is cut off. The network topology update rule is as follows: （6） The isolated node no longer participates in any neighbor-driven propagation or transfer, but its state is still continuously tracked for evaluation; Defining the prevalence of an epidemic For a moment t In the original node set V The above statistics show the number of infections; the optimal intervention strategy a = { a 0 , a 1 , . . . , a T The objective of solving 1} is: （7） The constraints are , ;exist T = B Under this setting, each step isolates exactly one node, and the budget constraint is automatically satisfied by the constructor.

5. The method as described in claim 4, characterized in that, Step S2 further includes: The above problem can be modeled as a finite-time Markov decision process: state: S t = (Z t , b t ),in This is the state-aware embedding matrix for each active node at the current moment. b t = B t Provide the strategy with a clear, limited temporal awareness of the remaining intervention steps; action: a t ∈ V t That is, select one node from the set of active nodes to perform isolation; award: R t = N I ( t + 1), maximizing the cumulative reward is directly aligned with minimizing the infection in the objective function (7); State transition: during the execution of an action a t Afterwards, the network topology is updated according to equation (6), and then the rumors and epidemic dynamics propagate on the updated topology according to equations (2)–(5), generating new node states to construct the state for the next time step. S t+1 .

6. The method as described in claim 5, characterized in that, Step S3 includes: The CLA encoder transforms the heterogeneous structure and interdependencies of a two-layer network into a high-level state-aware node representation through three stages: (1) Construction of node features For time t Each node i Construct the input feature vector: （8） in and These are the structural features (including topological statistics such as degree and centrality) calculated on the current active topologies of the epidemic layer and the rumor layer, respectively; i ( t This refers to the one-hot encoding concatenation of the node's two-layer state: （9） This construction ensures a two-layer state space. S ( r ) × S ( e The semantics of ) are preserved and effectively utilized; (2) In-layer multi-head graph attention network Two parallel multi-head graph attention networks (GAT) are used to focus on the epidemic layer. and rumor layer Extract the structural patterns within the layers, and maintain independent parameters for each layer to preserve semantic distinction; Node embeddings are initialized via learnable linear projections: （10） node i In the layer No. l The feature update rule for layer +1 is: （11） in H For the number of attention heads, To quantify neighbor nodes j For nodes i Attention coefficient of importance; L After layer graph attention, the final embeddings of each layer are obtained. and The corresponding layer feature matrix H (e) ( t ) and H (r) ( t ); (3) Adaptive cross-layer attention fusion To capture the heterogeneity of node roles across different layers, an adaptive gating mechanism is introduced to dynamically fuse the two decoupled representations: First, concatenate the two embedded layers and compute the soft-gating attention weights: （12） in, Soft gating weights are used to control information flow at each layer; Then, the weighted fusion embedding is calculated: （13） Finally, the final state-aware node representation is obtained through nonlinear refinement: （14） The final output node representation matrix It provides a high-level, real-time state-aware representation of the cooperative evolution network for reinforcement learning agents.

7. The method as described in claim 6, characterized in that, Step S4 includes: Based on the node representation matrix Z generated in step S3 t The Actor network computes the logit value of each node by sharing an MLP: （15） in g θ ( · This is a shared MLP applied node-by-node; to ensure sampling of valid actions, a binary mask m is defined. t :when i ∈ V t hour m i ( t ) = 1, otherwise m i ( t ) = 0; Action probability is calculated using a mask Softmax: （16） The Critic network first embeds variable-length nodes into matrix Z. t The representation is compressed into a fixed-dimensional graph level by permutation-invariant mean / sum pooling, and then the output state value is estimated by a lightweight MLP. V ψ ( S t ), used for PPO updates.

8. The method as described in claim 7, characterized in that, Step S4 further includes: To address the state space explosion problem in large-scale heterogeneous networks, a course learning strategy is introduced, dividing the training process into... K Each stage k ∈ {1 , . . . ,K } Corresponding task tuple M (k) = ( N (k) , T (k) , Θ (k) ), specify the network size, topology type, and propagation dynamics parameters respectively; The course difficulty increases progressively along two main dimensions: (1) Increasing scale: N (1) < N (2) < · · · < N (K) This guides intelligent agents to gradually adapt to large-scale networks from small-scale networks. (2) Structural heterogeneity: topological type T (k) The model evolves from random homogeneous networks to structurally heterogeneous networks with high clustering coefficients or heavy-tailed distributions, allowing it to first master basic dynamic operators in symmetric networks and then transition to complex topologies where structural heterogeneity has a nonlinear impact on the co-evolution of rumors and the pandemic.

9. A dynamic intervention system for key nodes of a three-dimensional spatial epidemic transmission supernetwork, characterized in that, The system includes a co-evolutionary modeling module, a decision process framework establishment module, a cross-layer attention encoding module, and an intervention strategy training module, among which: The co-evolution modeling module is used to model the collaborative propagation process of rumors and epidemics in the information-physical-social ternary space as a two-layer network: the rumor propagation network in the information space composed of social media platforms is the rumor layer, and the disease propagation network in the physical space composed of physical contact networks is the epidemic layer; the node set is embedded into two undirected graphs with different topological structures at the same time, and the state transition probability and cross-layer coupling mechanism of each node in the two layers are defined respectively to characterize the two-way dynamic feedback between the information space and the physical space through individual behavior in the social space; The decision process framework establishment module is used to formalize the intervention task into a dynamic key node control problem under budget constraints, establish a finite time domain Markov decision process framework, take minimizing the cumulative number of infected people in the control time domain as the optimization objective, and select one node from the active node set for isolation in each step until the global budget is exhausted. The cross-layer attention encoding module is used to construct a node feature vector that includes topological statistical features and node state one-hot encoding. It uses an intra-layer multi-head graph attention network with independent parameters to extract node embeddings from the rumor layer and the epidemic layer respectively. Then, it integrates the two layers of embeddings into a state-aware node representation matrix through an adaptive cross-layer attention fusion mechanism. The intervention strategy training module is used to train sequence intervention strategies based on the near-end policy optimization algorithm. It ensures that each step only samples legal actions from the active node set through mask Softmax. It also adopts an adaptive course learning strategy, which gradually increases the complexity of the training task in the order of increasing network size and increasing topology from homogeneous to heterogeneous. Knowledge transfer is achieved through cross-stage parameter inheritance, thereby improving the stability of policy training and cross-scale generalization ability.

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