Rumor propagation model construction method, rumor propagation inhibition method, computer equipment and storage medium

Abstract

The invention discloses a rumor propagation model construction method, a rumor propagation inhibition method, computer equipment and a storage medium in the technical field of temporal network propagation dynamics. The rumor propagation model construction method comprises the following steps: describing memory dependence of an individual on current information judgment by using a fractional derivative; introducing the fractional order derivative into an activity driven SIR rumor propagation model, and establishing a fractional order rumor propagation model; and in combination with a network topology structure and time-varying characteristics of attributes of nodes, describing node activity rate changes in the fractional order rumor propagation model by using a standard wiener process, and obtaining the rumor propagation model. According to the rumor propagation model construction method, the time-varying characteristics of the individual memory effect and the node activity rate in the current social network are combined, so that the rumor propagation model better fits the real situation, a theoretical basis is provided for analysis and control of rumor propagation, and prevention and control of propagation of malicious public opinions are facilitated.

Description

Technical Field

[0001] The present invention relates to a rumor propagation model construction method, a rumor propagation suppression method, a computer device and a storage medium, and belongs to the technical field of temporal network propagation dynamics. Background Art

[0002] A temporal network is a network system in which nodes and connections (i.e., edges) depend not only on their structural relationships but also on time. For example, transportation networks, power networks, financial transaction networks, communication networks, supply chain networks, infectious disease and rumor propagation networks, etc. are all temporal networks.

[0003] Communication dynamics is a scientific field that studies the patterns and mechanisms of disease or information transmission in a group. Its core lies in understanding the contact patterns between individuals and the effects of various control strategies. By establishing and analyzing the communication model, the possibility, scope and duration of rumor spread can be predicted, thus providing a scientific basis for public information management. By accurately constructing the communication model, the propagation path, speed and influencing factors of the rumor can be deeply analyzed, so as to predict its diffusion range, duration and potential social impact, and formulate effective intervention strategies to control its spread. Therefore, reasonable network modeling and control, and theoretical and numerical research on this basis are important research methods in current communication dynamics.

[0004] In general, existing research is mainly based on static networks. Considering the temporal characteristics of real networks, Perra first proposed an activity-driven network. This activity-driven network is highly parameterized and encapsulates the complex interactions between agents and interactions as the activity rate of nodes. However, in a real network, each individual has a certain memory, and the individual's judgment of current information depends on his previous memory; and there are various uncertainties in the real world, such as changes in network topology, the randomness of individual behavior, the influence of external environmental factors, and the randomness of the infection process. Therefore, the classic activity-driven network model is too idealized and cannot well describe the rumor diffusion behavior in temporal networks.

[0005] In addition, the spread of rumors can cause great harm to society. It can not only quickly cause social panic and lead to the disorder of public order, but also intensify social conflicts and cause collective behavior to get out of control. Moreover, the spread of rumors may mislead the public and make them make wrong decisions, interfere with emergency response and rescue operations, and delay the transmission of key information. However, at present, in the known temporal networks, only the propagation suppression of integer-order rumors in temporal networks is considered, and the control of rumor propagation in random fractional-order temporal networks is not considered. Summary of the invention

[0006] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for constructing a rumor propagation model that is more in line with reality. It also provides a rumor propagation suppression method, computer equipment and storage medium that can suppress the spread of rumors.

[0007] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0008] In a first aspect, the present invention provides a method for constructing a rumor propagation model, the method comprising:

[0009] Fractional derivatives are used to describe the memory dependence of individuals' judgments on current information;

[0010] The fractional-order derivative is introduced into the activity-driven SIR rumor propagation model to establish a fractional-order rumor propagation model;

[0011] Combined with the time-varying characteristics of the network topology and the node's own attributes, the standard Wiener process is used to describe the changes in the node activity rate in the fractional-order rumor propagation model to obtain the rumor propagation model.

[0012] In combination with the first aspect, optionally, the fractional-order derivative is a Caputo fractional-order derivative; the expression of the fractional-order rumor propagation model is as follows:

[0013] (1)

[0014] in represents the probability that node i is a healthy node at time t, represents the probability that node i is a rumor spreading node at time t, represents the probability that node i is an immune node at time t, , , Respectively express , , Find the order The left Caputo-type fractional derivative of , represents the fractional order, represents the probability that a healthy node becomes a rumor propagation node when it contacts a rumor propagation node, represents the probability that the rumor propagation node becomes an immune node when the rumor propagation node contacts the immune node, Represents the total number of nodes in the network, represents the activity rate of node i, Representation Node activity rate, represents a node set, Indicates that at time t the node is the probability of a rumor spreading node; the healthy node refers to a node in the network that has not received rumor information and is in an unknown state to the rumor information; the rumor spreading node refers to a node in the network that has received rumor information and is in a rumor spreading state; the immune node refers to a node in the network that has received rumor information and does not believe in the rumor information and does not spread rumors.

[0015] In combination with the first aspect, optionally, the rumor propagation model is expressed as follows:

[0016]

[0017] in, Indicates the noise intensity;

[0018] represents the standard Wiener process corresponding to node i at time t;

[0019] represents the standard Wiener process corresponding to node j at time t;

[0020] represents the probability that the disturbed node i is activated and actively connected to other nodes at time t;

[0021] represents the probability that node j is connected to other activated nodes that are disturbed at time t;

[0022] Represents the sum of the probabilities of active infection and passive infection of node i at time t.

[0023] In a second aspect, the present invention provides a method for suppressing the spread of rumors, the method comprising:

[0024] Get pre-built rumor propagation models;

[0025] A control variable for suppressing rumor propagation is introduced into the rumor propagation model to obtain a controlled fractional-order SIR rumor propagation model;

[0026] Based on the control variables, a target universal function is constructed with the goal of minimizing the average probability of rumor propagation nodes in the controlled fractional-order SIR rumor propagation model;

[0027] Finding the optimal solution of the objective universal function and obtaining the optimal control signal;

[0028] Suppressing rumor propagation based on the optimal control signal;

[0029] Among them, the rumor propagation model is constructed and obtained using any method described in the first aspect.

[0030] In conjunction with the second aspect, optionally, the control variables include the intensity of implementing a restriction strategy to suppress the spread of rumors and the intensity of implementing a prevention strategy to suppress the spread of rumors;

[0031] The expression of the controlled fractional-order SIR rumor propagation model is as follows:

[0032]

[0033] The expression of the objective functional is as follows:

[0034] ;

[0035] in: represents the probability that node i is a healthy node at time t, represents the probability that node i is a rumor spreading node at time t, represents the probability that node i is an immune node at time t, , , Respectively express , , Find the order The left Caputo-type fractional derivative of , represents the fractional order, represents the probability that a healthy node becomes a rumor propagation node when it contacts a rumor propagation node, represents the probability that the rumor propagation node becomes an immune node when the rumor propagation node contacts the immune node, Represents the total number of nodes in the network, represents the activity rate of node i, Representation Node activity rate, represents a node set, Indicates that at time t the node The probability of being a rumor spreading node; Indicates the noise intensity; represents the standard Wiener process corresponding to node i at time t; represents the standard Wiener process corresponding to node j at time t; It represents the intensity of the restriction strategy implemented on node i at time t, and its effect on the activity rate is in the form of ; represents the intensity of the prevention strategy implemented on node i at time t;

[0036] Is Composition dimensional column vector, Is Composition dimension column vector, and , To allow the control signal set, , represents the probability that node N is a rumor spreading node at time t, Indicates the cutoff time, is a system where all elements are of dimensional column vector, represents the transpose operation, represents the expected number of rumor spreading nodes at time t, is a positive scalar, and is a constant positive definite diagonal matrix, and They are all normal numbers;

[0037] The healthy node refers to a node in the network that has not received rumor information and is in an unknown state to the rumor information; the rumor propagation node refers to a node in the network that has received rumor information and is in a rumor propagation state; the immune node refers to a node in the network that has received rumor information and does not believe in the rumor information and does not propagate rumors.

[0038] In conjunction with the second aspect, optionally, finding the optimal solution of the target universal function includes:

[0039] The Pontryagin minimum principle is used to find the optimal solution of the objective universal function.

[0040] In a third aspect, the present invention provides a computer device, comprising a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the method described in any one of the first aspect or the second aspect are performed.

[0041] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any one of the first aspect or the second aspect.

[0042] In a fifth aspect, the present invention provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the method described in any one of the first aspect or the second aspect.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) The rumor propagation model construction method provided by the present invention is based on the traditional activity-driven SIR rumor propagation model, combined with the individual memory effect and the time-varying characteristics of the node activity rate in today's social networks to construct a rumor propagation model. The rumor propagation model is more in line with the actual situation and more accurately describes the rumor propagation behavior in the temporal network. It provides a theoretical basis for the analysis and control of rumor propagation, and helps to prevent and control the spread of malicious public opinion.

[0045] (2) The rumor propagation suppression method provided by the present invention is based on the aforementioned rumor propagation model. The rumor propagation behavior is controlled by introducing control variables that suppress the spread of rumors. A target function is constructed with the goal of minimizing the average probability of rumor propagation nodes in the controlled fractional-order SIR rumor propagation model. The optimal control signal is obtained by solving the optimal solution of the target function, so that as many healthy nodes as possible are transformed into immune nodes, thereby reducing the number of rumor propagation nodes in the network as much as possible, thereby achieving the purpose of suppressing the outbreak of rumors and controlling the spread of rumors. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of a method for constructing a rumor propagation model provided in Embodiment 1 of the present invention;

[0047] Figure 2 is a flow chart of a method for suppressing rumor propagation provided by Embodiment 2 of the present invention;

[0048] Figure 3 is the average probability of rumor spreading nodes when only memory is considered without considering node activity rate interference and optimal control signal The dynamic process of change;

[0049] Figure 4 It is a fractional order The average probability of rumor propagation nodes before and after adding random interference Comparison chart of changes over time;

[0050] Figure 5 is the fractional order under random interference The average probability of healthy nodes before and after adding the optimal control signal Comparison chart of changes over time;

[0051] Figure 6 is the fractional order under random interference The average probability of rumor propagation nodes before and after adding the optimal control signal Comparison chart of changes over time;

[0052] Figure 7 is the fractional order under random interference The average probability of immune nodes before and after adding the optimal control signal Comparison chart of changes over time;

[0053] Figure 8 It is a schematic diagram of the internal structure of a computer device provided in Embodiment 3 of the present invention. DETAILED DESCRIPTION

[0054] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations on the technical solution of the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0055] Embodiment 1:

[0056] Figure 1 This is a flow chart of a rumor propagation model construction method in the first embodiment of the present invention. This flow chart only shows the logical sequence of the method described in this embodiment. In other possible embodiments of the present invention, different methods may be used without conflict. Figure 1 The steps shown or described are accomplished in the order shown.

[0057] The rumor propagation model construction method provided in this embodiment mainly includes the following steps:

[0058] Step 101: Using fractional derivatives to describe the memory dependence of an individual's judgment on current information;

[0059] In a real network, each individual has a certain memory, and the individual's judgment of the received information depends on his previous memory. Studies have shown that fractional derivatives can describe the memory effect in the dynamics of online social networks. Therefore, in the embodiment of the present invention, fractional derivatives are introduced into the rumor propagation model to describe the memory dependence of individuals on the current information judgment.

[0060] Step 102: Introducing the fractional-order derivative into the activity-driven SIR rumor propagation model to establish a fractional-order rumor propagation model;

[0061] The SIR rumor propagation model is a rumor propagation model based on the SIR model. The SIR model (Susceptible- Infected- Removed) is actually an infectious disease model based on social networks. It is used to describe the process of disease transmission in which infected individuals become immune after being cured, thus becoming healthy individuals and will not be infected again, or die due to difficulty in curing, thus moving out of the transmission system and no longer infecting other individuals. Considering the similarity between information propagation and biological virus propagation, the SIR model can effectively simulate the evolution of network rumor propagation. In the SIR model, user states can be divided into three categories: susceptible S, infected I, and immune R (removed individual). The proportion of user in-and-out degrees represents their influence, and the network topology structure characteristics are pointed out, including scale-free characteristics, information propagation characteristics, and the maximum propagation time of rumors.

[0062] Step 103: combining the network topology and the time-varying characteristics of the node's own attributes, using the standard Wiener process to describe the change in the node activity rate in the fractional-order rumor propagation model, and obtaining the rumor propagation model.

[0063] In the network topology structure based on rumor propagation, nodes are used to represent users, and edges are used to represent information propagation between connected nodes. According to the different states of users in the network topology structure, nodes can be divided into three categories: healthy nodes, rumor propagation nodes, and immune nodes. Among them, healthy nodes correspond to susceptible nodes in the SIR model, which refer to nodes in the network that have not received rumor information and are in an unknown state to the rumor information; rumor propagation nodes correspond to infected nodes in the SIR model, which refer to nodes in the network that have received rumor information and are in a rumor propagation state; immune nodes correspond to immune nodes in the SIR model, which refer to nodes in the network that have received rumor information but do not believe in the rumor information and do not spread rumors.

[0064] Due to various uncertain factors in the real world, the properties of any node may change over time. In this embodiment, the time-varying characteristics of the node's own properties refer to the dynamic process of the properties of a node in the network changing over time. Specifically, these properties include the state, weight, connection strength, activity, propagation ability, etc. of the node, which will continue to change over time under the influence of network evolution or external factors.

[0065] The time-varying characteristics of healthy nodes include infection probability and state transition. Over time, the probability of healthy nodes being infected by rumors and turning into rumor spreading nodes will change, depending on their contact frequency with rumor spreading nodes, their spread power, and the effectiveness of protective measures. Healthy nodes may become rumor spreading nodes at some point in time, and this state transition will change over time.

[0066] The time-varying characteristics of rumor propagation nodes include propagation capacity and propagation intensity. The propagation capacity of rumor propagation nodes may change over time, affected by their activity, influence, or the overall intensity of rumor propagation in the network. The intensity of rumor propagation by rumor propagation nodes at a certain moment may change over time, which may be affected by factors such as node fatigue and external intervention.

[0067] In the embodiment of the present invention, the node activity rate is encapsulated by the complex interactions between agents and interactions. Therefore, according to the central limit theorem, the change of the standard Wiener process can be selected to characterize the change of the node activity rate.

[0068] In summary, the rumor propagation model construction method provided by the embodiment of the present invention is based on the traditional activity-driven SIR rumor propagation model, combined with the time-varying characteristics of individual memory effect and node activity rate in today's social networks to construct a rumor propagation model. The rumor propagation model is more in line with the actual situation and more accurately describes the rumor propagation behavior in the temporal network. It provides a theoretical basis for the analysis and control of rumor propagation, and helps to prevent and control the spread of malicious public opinion.

[0069] As an embodiment of the present invention, in step 102, the fractional-order derivative may be a Caputo fractional-order derivative. For this purpose, the expression of the fractional-order rumor propagation model is as follows:

[0070] (1)

[0071] in represents the probability that node i is a healthy node at time t, represents the probability that node i is a rumor spreading node at time t, represents the probability that node i is an immune node at time t, , , Respectively express , , Find the order The left Caputo-type fractional derivative of , represents the fractional order, represents the probability that a healthy node becomes a rumor propagation node when it contacts a rumor propagation node, represents the probability that the rumor propagation node becomes an immune node when the rumor propagation node contacts the immune node, Represents the total number of nodes in the network, represents the activity rate of node i, Representation Node activity rate, represents a node set, Indicates that at time t the node The probability of being a rumor spreading node.

[0072] For step 103, according to the central limit theorem, a variation of the standard Wiener process is selected To describe the changes in node activity rate, the expression of the rumor propagation model can be obtained as follows:

[0073]

[0074] in, Indicates the noise intensity;

[0075] represents the standard Wiener process corresponding to node i at time t;

[0076] represents the standard Wiener process corresponding to node j at time t;

[0077] represents the probability that the disturbed node i is activated and actively connected to other nodes at time t;

[0078] represents the probability that node j is connected to other activated nodes that are disturbed at time t;

[0079] Represents the sum of the probabilities of active infection and passive infection of node i at time t.

[0080] The rumor propagation model construction method provided in this embodiment can be applied to a terminal and can be executed by a rumor propagation model construction device, which can be implemented by software and / or hardware, and the device can be integrated in a terminal, for example: any smart phone, tablet computer or computer device with communication function.

[0081] Embodiment 2:

[0082] Figure 2 This is a flow chart of a rumor propagation suppression method provided by Example 2 of the present invention. The method provided by this embodiment can be implemented based on the rumor propagation model constructed in Example 1. For technical contents related to the construction of the rumor propagation model, please refer to Example 1.

[0083] like Figure 2 As shown, the rumor propagation suppression method provided in this embodiment specifically includes the following steps:

[0084] Step 201: Obtain a pre-built rumor propagation model;

[0085] The rumor propagation model is constructed and obtained using the method described in the first embodiment above.

[0086] Step 202: introducing a control variable for suppressing rumor propagation into the rumor propagation model to obtain a controlled fractional-order SIR rumor propagation model;

[0087] Suppress the spread of rumors through the following two aspects:

[0088] On the one hand, the probability of active infection among susceptible people can be reduced through social norms and regulatory enforcement, and the probability of passive infection among susceptible people can be reduced through isolation measures, thereby reducing the probability of these people (corresponding to healthy nodes) being infected and becoming people with the ability to spread rumors (corresponding to rumor spreading nodes). Therefore, the first control variable is introduced, which represents the intensity of the restriction strategy implemented on the node.

[0089] On the other hand, another effective measure to reduce the spread of rumors is to spread anti-rumor information to people who are susceptible to infection, so that these people (corresponding to healthy nodes) are directly transformed into immune people (corresponding to immune nodes). Therefore, a second control variable is introduced, which represents the intensity of the prevention strategy implemented at the node.

[0090] The above two control variables are introduced into the rumor propagation model as control variables for suppressing the spread of rumors to obtain a controlled fractional-order SIR rumor propagation model.

[0091] Step 203: Based on the control variables, a target universal function is constructed with the goal of minimizing the average probability of rumor propagation nodes in the controlled fractional-order SIR rumor propagation model;

[0092] Based on the control variables for suppressing the spread of rumors, a target functional is established. Through subsequent optimization of the target functional, that is, finding parameters that can minimize the functional, the parameters obtained by optimizing the target functional are introduced into the controlled fractional-order SIR rumor propagation model, so that the average probability of rumor propagation nodes in the controlled fractional-order SIR rumor propagation model is minimized.

[0093] Step 204: finding the optimal solution of the objective universal function and obtaining the optimal control signal;

[0094] When the functional of the objective function reaches a minimum value, the control variable that makes the functional reach the minimum value is the optimal control signal. The optimal control signal includes two control variables. The first control variable represents the optimal intensity of implementing a restriction strategy at a node, and the second control variable represents the optimal intensity of implementing a prevention strategy at a node.

[0095] Step 205: Suppress rumor propagation based on the optimal control signal.

[0096] The optimal control signal obtained through the above steps is introduced into the controlled fractional-order SIR rumor propagation model, and rumor propagation suppression is performed based on the model, thereby effectively suppressing the probability peak of healthy nodes being infected and controlling the probability of healthy nodes being transformed into rumor propagation nodes.

[0097] As an embodiment of the present invention, the control variables include the intensity of implementing a restriction strategy to suppress the spread of rumors and the intensity of implementing a prevention strategy to suppress the spread of rumors;

[0098] The expression of the controlled fractional-order SIR rumor propagation model is as follows:

[0099]

[0100] The expression of the objective functional is as follows:

[0101] ;

[0102] in: represents the probability that node i is a healthy node at time t, represents the probability that node i is a rumor spreading node at time t, represents the probability that node i is an immune node at time t, , , Respectively express , , Find the order The left Caputo-type fractional derivative of , represents the fractional order, represents the probability that a healthy node becomes a rumor propagation node when it contacts a rumor propagation node, represents the probability that the rumor propagation node becomes an immune node when the rumor propagation node contacts the immune node, Represents the total number of nodes in the network, represents the activity rate of node i, Representation Node activity rate, represents a node set, Indicates that at time t the node The probability of being a rumor spreading node; Indicates the noise intensity; represents the standard Wiener process corresponding to node i at time t; represents the standard Wiener process corresponding to node j at time t; It represents the intensity of the restriction strategy implemented on node i at time t, and its effect on the activity rate is in the form of ; represents the intensity of the prevention strategy implemented on node i at time t;

[0103] Is Composition dimensional column vector, Is Composition dimension column vector, and , To allow the control signal set, , represents the probability that node N is a rumor spreading node at time t, Indicates the cutoff time, is a system where all elements are of dimensional column vector, represents the transpose operation, represents the expected number of rumor spreading nodes at time t, is a positive scalar, and is a constant positive definite diagonal matrix, and They are all normal numbers;

[0104] The healthy node refers to a node in the network that has not received rumor information and is in an unknown state to the rumor information; the rumor propagation node refers to a node in the network that has received rumor information and is in a rumor propagation state; the immune node refers to a node in the network that has received rumor information and does not believe in the rumor information and does not propagate rumors.

[0105] As an embodiment of the present invention, the Pontryagin minimum principle is used to find the optimal solution of the objective universal function. Specifically, a Hamiltonian function is constructed in combination with the objective universal function, and the optimal solution of the objective universal function is found according to the Pontryagin minimum principle, that is, at each time t, by solving the minimization problem of the Hamiltonian function, the optimal control signal that minimizes the objective universal function value is determined.

[0106] The following uses MATLAB simulation software to simulate the rumor propagation process and analyze the simulation results:

[0107] In this embodiment, in order to better analyze the random fractional-order rumor propagation model established in the activity-driven network, the rumor propagation model is pre-established on the Superuser network using the method described in Example 1, wherein the Superuser data set contains a total of 3711 nodes, the average activity rate is 0.2286, and the scaling index is 2.5378. During the rumor propagation process, according to the rumor propagation model established in Example 1, the individual is in any one of the susceptible state, propagation state, and immune state. In order to avoid the influence of accidental errors, the simulation results of each experiment in this embodiment are the average results of more than 200 runs.

[0108] Figure 3 is the average probability of rumor spreading nodes when only memory is considered without considering node activity rate interference and optimal control signal The dynamic process of change. Figure 3 It can be seen that the fractional order The smaller the size, the stronger the corresponding individual memory effect, and the fractional order The larger it is, the weaker the corresponding individual memory effect is. Corresponding to the traditional activity-driven network. The stronger the individual's memory effect, the average probability of the rumor propagation node The later the peak is reached, and the average probability of rumor propagation nodes The smaller the peak value, the more it can suppress the outbreak of rumors.

[0109] Figure 4 It is a fractional order The average probability of rumor propagation nodes before and after adding random interference A comparison of changes over time. Figure 4 , the average probability of rumor spreading nodes after adding random interference is compared with that before adding random interference. The peak value is smaller and The peak time of the rumor also occurs earlier, which can reduce the scale of rumor spread and suppress the outbreak of rumors.

[0110] Figure 5 is the fractional order under random interference The average probability of healthy nodes before and after adding the optimal control signal Comparison of changes over time. The average probability of healthy nodes after adding the optimal control signal is compared with before adding the optimal control signal. It is declining rapidly. These healthy nodes are successfully transformed into immune nodes through social norms, regulatory enforcement, isolation measures and the release of anti-rumor information. The immune nodes have a sufficient level of awareness of rumors and are immune to them and will no longer spread rumor information.

[0111] Figure 6 is the fractional order under random interference The average probability of rumor propagation nodes before and after adding the optimal control signal Comparison of changes over time. The average probability of rumor propagation nodes before adding the optimal control signal is increasing rapidly; and after adding the optimal control signal, Figure 6 As can be seen from the figure, the average probability of rumor propagation nodes It is slowly decreasing and is much smaller than before adding the optimal control signal. This is because many healthy nodes are transformed into immune nodes after being affected by social norms, regulatory enforcement, isolation measures and anti-rumor information. Therefore, the number of healthy nodes that are susceptible to rumors has decreased accordingly, and naturally, the number of healthy nodes that have turned into rumor-spreading nodes has also decreased.

[0112] Figure 7 is the fractional order under random interference The average probability of immune nodes before and after adding the optimal control signal Comparison of changes over time. The average probability of immune nodes before adding the optimal control signal is rising slowly; and after adding the optimal control signal, Figure 7 As can be seen in Figure 2, the number of immune nodes increases rapidly and is much larger than the number before adding the optimal control variable. Because immune nodes have sufficient knowledge of rumors and are immune, they will not spread rumors.

[0113] Embodiment three:

[0114] The embodiment of the present invention further provides a computer device, which may be a server, and its internal structure diagram may be as shown in FIG. Figure 8As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store data obtained and generated in the method of embodiment one or embodiment two. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the method of the aforementioned embodiment one or two is implemented.

[0115] Those skilled in the art will understand that Figure 8 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0116] The computer device provided in the embodiment of the present invention can execute the method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0117] Embodiment 4:

[0118] An embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the method of the above-mentioned embodiment 1 or embodiment 2 are first implemented.

[0119] The computer-readable storage medium includes: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and other media that can store program codes.

[0120] Embodiment five:

[0121] An embodiment of the present invention further provides a computer program product, including a computer program / instruction, which implements the steps of the method of embodiment 1 or embodiment 2 when executed by a processor.

[0122] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0123] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0124] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0125] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0126] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for constructing a rumor propagation model, characterized in that: The method comprises: Fractional derivatives are used to describe the memory dependence of individuals' judgments on current information; The fractional-order derivative is introduced into the activity-driven SIR rumor propagation model to establish a fractional-order rumor propagation model; Combined with the time-varying characteristics of the network topology and the node's own attributes, the standard Wiener process is used to describe the changes in the node activity rate in the fractional-order rumor propagation model to obtain the rumor propagation model.

2. The method according to claim 1, characterized in that The fractional-order derivative is the Caputo fractional-order derivative; the expression of the fractional-order rumor propagation model is as follows: （1）； in represents the probability that node i is a healthy node at time t, represents the probability that node i is a rumor spreading node at time t, represents the probability that node i is an immune node at time t, , , Respectively express , , Find the order The left Caputo-type fractional derivative of , represents the fractional order, represents the probability that a healthy node becomes a rumor propagation node when it contacts a rumor propagation node, represents the probability that the rumor propagation node becomes an immune node when the rumor propagation node contacts the immune node, Represents the total number of nodes in the network, represents the activity rate of node i, Representation Node activity rate, represents a node set, Indicates that at time t the node is the probability of a rumor spreading node; the healthy node refers to a node in the network that has not received rumor information and is in an unknown state to the rumor information; the rumor spreading node refers to a node in the network that has received rumor information and is in a rumor spreading state; the immune node refers to a node in the network that has received rumor information and does not believe in the rumor information and does not spread rumors.

3. The method according to claim 2, characterized in that The expression of the rumor propagation model is as follows: ； in, Indicates the noise intensity; represents the standard Wiener process corresponding to node i at time t; represents the standard Wiener process corresponding to node j at time t; represents the probability that the disturbed node i is activated and actively connected to other nodes at time t; represents the probability that node j is connected to other activated nodes that are disturbed at time t; Represents the sum of the probabilities of active infection and passive infection of node i at time t.

4. A method for suppressing rumor propagation, characterized in that: The method comprises: Get pre-built rumor propagation models; A control variable for suppressing rumor propagation is introduced into the rumor propagation model to obtain a controlled fractional-order SIR rumor propagation model; Based on the control variables, a target universal function is constructed with the goal of minimizing the average probability of rumor propagation nodes in the controlled fractional-order SIR rumor propagation model; Finding the optimal solution of the objective universal function and obtaining the optimal control signal; Suppressing rumor propagation based on the optimal control signal; Wherein, the rumor propagation model is constructed and obtained by using the method described in any one of claims 1 to 3.

5. The method according to claim 4, characterized in that The control variables include the intensity of implementing restriction strategies to suppress rumor spreading and the intensity of implementing prevention strategies to suppress rumor spreading; The expression of the controlled fractional-order SIR rumor propagation model is as follows: ； The expression of the objective functional is as follows: ； in: represents the probability that node i is a healthy node at time t, represents the probability that node i is a rumor spreading node at time t, represents the probability that node i is an immune node at time t, , , Respectively express , , Find the order The left Caputo-type fractional derivative of , represents the fractional order, represents the probability that a healthy node becomes a rumor propagation node when it contacts a rumor propagation node, represents the probability that the rumor propagation node becomes an immune node when the rumor propagation node contacts the immune node, Represents the total number of nodes in the network, represents the activity rate of node i, Representation Node activity rate, represents a node set, Indicates that at time t the node The probability of being a rumor spreading node; Indicates the noise intensity; represents the standard Wiener process corresponding to node i at time t; represents the standard Wiener process corresponding to node j at time t; It represents the intensity of the restriction strategy implemented on node i at time t, and its effect on the activity rate is in the form of ; represents the intensity of the prevention strategy implemented on node i at time t; Is Composition dimensional column vector, Is Composition dimension column vector, and , To allow the control signal set, , represents the probability that node N is a rumor spreading node at time t, Indicates the cutoff time, is a matrix whose elements are all 1. dimensional column vector, represents the transpose operation, represents the expected number of rumor spreading nodes at time t, is a positive scalar, and is a constant positive definite diagonal matrix, and They are all normal numbers; The healthy node refers to a node in the network that has not received rumor information and is in an unknown state to the rumor information; the rumor propagation node refers to a node in the network that has received rumor information and is in a rumor propagation state; the immune node refers to a node in the network that has received rumor information and does not believe in the rumor information and does not propagate rumors.

6. The method according to claim 4 or 5, characterized in that: The step of finding the optimal solution of the target universal function comprises: The Pontryagin minimum principle is used to find the optimal solution of the objective universal function.

7. A computer device, characterized in that: The method comprises a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the method according to any one of claims 1 to 6 are executed.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method described in any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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