A modeling and simulation method for infectious disease transmission based on temporal network

Abstract

This paper discloses a modeling and simulation method for infectious disease transmission based on a time-series network. This method constructs a novel time-series network model with multiple interaction modes and uses this model to study the basic infectious disease transmission process. This method improves the time-series network model by distinguishing the interaction modes of ordinary nodes and leader nodes. The concept of leader nodes in the time-series network model takes into account the many-to-many interaction in real life. Combined with one-to-one interaction, this model better aligns with the operating mechanisms of real society. This method has important guiding significance for controlling the spread of disease and the dissemination of negative information.

Description

Technical Field

[0001] The present invention belongs to the field of computer simulation, and in particular relates to a modeling and simulation method for an infectious disease propagation model of a temporal network based on a leader mechanism. Background Art

[0002] Infectious diseases have always been a major concern for human society. With the development of society, humans began living in megacities with populations of tens of millions. Unprecedented living density and frequent social activities facilitated the rapid spread of infectious diseases within populations. Modern technology and the rapid development of rail, air, and automobile transportation have made human interaction easier and faster, but they have also accelerated the spread of infectious diseases and increased their impact. Historical pandemics and the ongoing outbreaks of infectious diseases in recent years demonstrate that each outbreak poses a significant threat to human health and property, even impacting human development.

[0003] The temporal network models used in many studies of infectious diseases on temporal networks are still similar to Perra's activity-driven model, that is, individuals interact with each other based on influencing factors. Petri proposed a simplex network that allows multiple individuals to interact in a simplex form, that is, group interactions occur. However, in society, real interactions are not simply one-to-one or many-to-many, but rather interactions between individuals and groups. Group activities are often related to the organizers of the activities, that is, most group activities are organized by the organizers of the activities. For example, professional curators will organize multiple exhibitions and tend to form groups and interact with multiple people. Ordinary people are more inclined to interact with each other. Based on this, the present invention mainly explores and constructs a new type of temporal network model with multiple interaction modes based on the social patterns in real life, and studies the basic infectious disease transmission process on this model, that is, a modeling and simulation method of infectious disease transmission model based on temporal networks, which can provide more accurate simulation data in simulating the infectious disease transmission process in real society. Summary of the Invention

[0004] The present invention overcomes the above-mentioned shortcomings of the prior art and provides a method for modeling and simulating an infectious disease propagation model based on a temporal network.

[0005] A modeling and simulation method for infectious disease transmission based on a time series network, the steps are as follows:

[0006] Step 1, obtaining an improved temporal network model;

[0007] First, an undirected graph is constructed in a two-dimensional spatial network, where each node is divided into a regular node and a leader node. Next, the number of leader activation nodes, n, is set. When a leader node is activated, it randomly selects n nodes, forming a connected subgraph of size s, in which n nodes and the leader node interact with each other. When a regular node is activated, only one node is randomly selected for interaction. All nodes i are assigned corresponding activity rates ai according to a power-law distribution, and a mapping is formed based on the activity rates. Finally, to determine the node type in the network, a probability function p(i) is developed that depends on the activity rate, representing the probability of a node being selected as a leader node.

[0008] Step 2: disease transmission;

[0009] Randomly select a node as the source of disease transmission, and use the number of infected people as an indicator of the severity of the infectious disease outbreak. Use the classic disease transmission model SIR to analyze the disease transmission in the time series network constructed in step 1. At the initial time t0, the source node is infected and becomes the source of transmission.

[0010] At each time step starting from t0, each node has a probability of being activated and interacting with other nodes. Before the next time step, all edges in the graph will be deleted.

[0011] The beneficial effects of the present invention are as follows:

[0012] This paper improves the temporal network model by distinguishing the interaction patterns between common nodes and leader nodes. The concept of leader nodes in the temporal network model takes into account the many-to-many interaction in real life. Combined with one-to-one interaction, this model better aligns with the operating mechanisms of real society. This has important guiding significance for controlling the spread of disease and the dissemination of negative information. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a schematic diagram of a two-dimensional spatial network node according to an embodiment of the present invention;

[0014] Figure 2 is a schematic diagram of an activated common node according to an embodiment of the present invention;

[0015] Figure 3 is a schematic diagram of an activated leader node according to an embodiment of the present invention;

[0016] Figure 4 This is a simulation comparison effect diagram of disease propagation using the temporal network model of the present invention and the traditional temporal network model. DETAILED DESCRIPTION

[0017] The technical solution of the present invention is further described below with reference to the accompanying drawings.

[0018] Figure 1 It is a number of nodes set up in a two-dimensional space network, where the nodes are divided into two categories: ordinary nodes and leader nodes;

[0019] Figure 2 This is a schematic diagram of a normal node being activated in the present invention. Node 4 is a normal node. When it is activated, it randomly selects a node, namely, node 5. Activating node 4 will interact with node 5 and create an edge with it in the current time step.

[0020] Figure 3 Figure 1 shows the activation of a leader node in the present invention. Node 1 is the leader node. When activated, it randomly selects n nodes, namely nodes 0, 4, and 5, to form a fully connected subgraph of size s, namely, subgraph {0, 1, 4, 5}. The activated node interacts with the other nodes and creates edges with them during the current time step.

[0021] A method for constructing a temporal network model, the specific construction steps are as follows:

[0022] Step 1, obtaining an improved temporal network model;

[0023] First, an undirected graph is constructed in a two-dimensional spatial network, where each node is divided into a regular node and a leader node. Next, the number of leader activation nodes, n, is set. When a leader node is activated, it randomly selects n nodes, forming a connected subgraph of size s, in which n nodes and the leader node interact with each other. When a regular node is activated, only one node is randomly selected for interaction. All nodes i are assigned corresponding activity rates ai according to a power-law distribution, and a mapping is formed based on the activity rates. Finally, to determine the node type in the network, a probability function p(i) is developed that depends on the activity rate, representing the probability of a node being selected as a leader node.

[0024] Step 2: disease transmission;

[0025] The classic disease propagation model SIR is used to propagate the disease in the above-constructed network. At the initial time t0, the above-selected nodes are infected and serve as the source of propagation.

[0026] In each time step starting from t0, each node has a probability of being activated and interacting with other nodes. Among them, when a normal node is activated, such as Figure 2 As shown in the figure, according to the traditional sequential network model, a node is randomly selected for interaction. When the leader node is activated, as shown in the figure, Figure 3As shown in Figure 1, the leader node randomly selects n nodes to form a connected subgraph of size s. The n nodes and the leader node interact with each other. Before the next time step, all edges in the connected subgraph will be deleted.

[0027] Reference Figure 4 , the temporal network model of the present invention is simulated and compared with the existing network model, and the following parameters are set for the disease transmission network: the number of nodes N = 2000, the activity rate ai obeys the Pareto distribution, where the exponent α = 2.4, the probability function p(i) is I[ai-p(x)>0)], where I is the indicator function, which is equal to 1 when ai-p(x)>0, otherwise equal to 0; p(x) is a uniform distribution in the range [0,1]. The number of nodes activated each time by the leader node is n = 4, the infection rate during disease transmission λ = 0.3, and the response rate μ = 0.05. The obtained infectious disease transmission model (LAD) based on the temporal network of the present invention and other network models show how the number of infected people changes with time steps. Figure 4 As shown. Among them, the AD model represents the activity-driven network, the SAD model represents the time series network where all nodes are leader nodes, the horizontal axis represents the time step of disease spread, and the vertical axis represents the proportion of infected people to the total population. Figure 4 As can be seen in the figure, the proportion of infected people gradually decreases over time, eventually approaching 0, indicating that the disease is under control. In the LAD network model, the speed and scope of disease spread are greater than in traditional time-driven networks. This shows that the presence of leader nodes makes the network more active, while the leader selection mechanism prevents the rapid outbreak of the disease as in the SAD model.

[0028] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A modeling and simulation method for infectious disease propagation based on a temporal network, characterized in that: Here are the steps: Step 1, obtaining an improved temporal network model; First, an undirected graph is set up in a two-dimensional spatial network, where each node of the undirected graph is divided into a normal node and a leader node. Second, the number of leader activation nodes n is set. When the leader node is activated, it randomly selects n nodes to form a connected subgraph of size s. The n nodes and the leader node interact with each other. When a normal node is activated, only one node is randomly selected for interaction. All nodes i obtain corresponding activity rates ai according to the power law distribution, and a mapping is formed based on the size of the activity rates. Finally, in order to determine the type of node in the network, a probability function p(i) that depends on the activity rate is formulated, which is expressed as the probability of a node being selected as a leader node. Step 2: disease transmission; Randomly select one node as the source of disease transmission, and use the number of infected people as an indicator to characterize the severity of the infectious disease outbreak. Use the classic disease transmission model SIR to study the disease transmission in the time series network constructed in step 1. At the initial time t0, the source node is infected and serves as the transmission source. In each time step starting from t0, each node has a probability of being activated and interacting with other nodes; before the next time step, all edges in the graph will be deleted.

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