CN108965287B - Virus propagation control method based on limited temporary edge deletion - Google Patents
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Abstract
A virus propagation control method based on finite temporary deletion edge constructs a virus propagation model, and establishes a susceptible-susceptible virus propagation model based on cellular automata; giving a network graph G (N, E), initializing an adjacent matrix A (t) of the network at the time t, and selecting m% of nodes as initial infection sources; utilizing a community structure discovery algorithm to obtain a deletion order based on the whole network edge betweenness; determining the number of edge deletion to be k% by using a breadth-first search algorithm, wherein k is a finite positive integer; temporarily deleting an edge meeting the condition according to the edge betweenness deletion sequence; repeating the previous step until the temporary edge deletion proportion is k%; the invention has the advantages of simplicity, effectiveness and obvious reduction of the virus transmission speed and the infection scale.
Description
Technical Field
The invention belongs to the technical field of computers, and particularly relates to a virus propagation control method based on limited temporary edge deletion.
Background
With the continuous development and development of the research on the complex network theory, more and more researchers pay attention to the dynamics of virus transmission on the complex network, such as virus transmission on computer network, rumor on social network, public opinion transmission, and disease transmission in biological network.
In real life, each individual has a behavior of being driving towards profit and avoiding harm, and as for nodes in the network, the individuals can avoid contacting infected nodes by changing the network structure. Thus, the topology of the network is no longer static.
In the research of Roc and the like, the edges directly connected with the important nodes or the edges between any two important nodes and the common neighbor nodes are immunized according to the relationship between the edges and the important nodes. Shaw et al and Gross et al both believe that when an infected node exists in the network, the vulnerable node will choose to disconnect from the infected node, and reselect a non-neighboring healthy node to connect with it to protect itself from infection. Risau-Gusman et al also studied the transmission behavior of the virus under various reconnecting methods. Later, Song Yurong et al in the course of research have demonstrated that the reconnecting method has an inhibitory effect on viral transmission. Cao Yulin et al analyzed the method proposed by Song Yurong et al and proposed a reconnection method based on shortest path and node degree. However, most of the existing optimization methods for controlling virus propagation all use edge deletion reconnection to control, but the cost of edge deletion reconnection is higher than that of only edge deletion, the realization is also more complicated, and limited resource constraints are not considered.
Disclosure of Invention
The invention aims to provide a virus propagation control method based on limited temporary deletion edge, which is simple, effective and capable of obviously reducing the virus propagation speed and the infection scale.
The technical scheme for solving the technical problems is as follows: a virus propagation control method based on limited temporary edge deletion comprises the following steps:
(1) construction of a Virus propagation model
Establishing a susceptible-susceptible virus propagation model based on a cellular automaton;
(2) giving a network graph G (N, E), wherein N represents a set of all nodes in the network, E represents a set of edges among all nodes in the network, initializing an adjacent matrix A (t) of the network at the time t, selecting m% of nodes as initial infection sources, and m is a finite positive integer;
(3) utilizing a community structure discovery algorithm to obtain a deletion order based on the whole network edge betweenness;
(4) determining the number of edge deletion to be k% by using a breadth-first search algorithm, wherein k is a finite positive integer;
(5) temporarily deleting an edge meeting the condition according to the edge betweenness deletion sequence obtained in the step (3);
(6) repeating the step (5) until the temporary edge deletion proportion is k%;
as a preferred technical solution, in the step (1), the nodes in the network are used as cells, the network including N nodes is a cellular automaton including N cells, N is a finite positive integer, and a susceptible-susceptible virus propagation model established according to four elements of the cellular automaton is:
cell space C: establishing a one-dimensional cellular space containing N cells at an initial moment;
finite state set Q: the states of the corresponding cells of the nodes are divided into a chromophil state and an infection state, which are respectively represented by 0 and 1, and a state set Q is {0, 1 }; si(t) is the state variable of the cell i at time t, Si(t) is equal to Q, then there is
Cell neighborhood V: the network adjacency matrix A (t) is the relation between each cell neighbor in the cell space, the neighbor of the cell i at the time t is the element set with all values of 1 in the ith row in A (t), alphaij＝1，αije.A (t) is the edge where there is a connection between cell i and cell j, and αii＝αjj＝0；
Cell state transition rule function δ: at each time t, the infected node infects neighboring nodes around the infected node with a probability beta, and the infected node is recovered to be a healthy node with a probability alpha, and the state transition function between the infected node and the healthy node is as follows:
in the formula, an upper horizontal line is an inversion operation, and g is a state transition judgment function between an infected node and an susceptible node;
the proportion of infected nodes at the time t is I (t),
when the proportion of healthy nodes at time t is s (t), at any time i (t) and s (t), i (t) + s (t) ═ 1 is satisfied.
As a preferred technical solution, the function for judging state transition between the infected node and the susceptible node
Wherein α represents a recovery rate, β represents an infection rate, γ is a random number between (0,1), and SjAnd (t) is the state variable of the unit cell j at the time t.
As a preferred technical scheme, the positions of m% nodes and the value of m are randomly selected.
The invention has the following beneficial effects:
compared with the prior art, the method has the advantages that the cost is low, the implementation is easy, and the virus propagation speed and the infection scale can be obviously reduced; the invention is a virus propagation control method irrelevant to the initial infection source, and can ensure that the basic functions of a network system are not influenced under the condition of temporarily deleting a limited number of edges. The method is simple and effective, has low cost and overhead, and can be used as a general optimization control method to be applied to the fields of public opinion network propagation control, traffic network congestion management and the like.
Drawings
FIG. 1 is a flowchart of a virus propagation control method based on limited temporary edge deletion according to the present invention.
FIG. 2 is a model of transmission of a susceptible-susceptible virus of the present invention.
Fig. 3 is a graph of the results of a simulation experiment of the infection rate of a small-scale actual network as a function of time.
FIG. 4 is a graph of simulation experiment results of WS networks' infection rates over time.
Fig. 5 is a diagram showing the results of a simulation experiment in which the average path length of a small-scale actual network varies with the number of punctured edges.
Fig. 6 is a graph of simulation experiment results of WS network average path length variation with number of punctured edges.
FIG. 7 is a diagram showing simulation experiment results of the change of the proportion of nodes in the maximum connected subgraph of the small-scale practical network along with the number of deleted edges.
FIG. 8 is a graph of simulation experiment results of the change of the proportion of nodes in the maximum connected subgraph of the WS network with the number of deleted edges.
Detailed Description
The present invention will be described in further detail below with reference to the drawings and examples, but the present invention is not limited to the embodiments described below.
In fig. 1, a virus propagation control method based on finite temporary edge deletion in this embodiment includes the following steps:
(1) establishing an SIS virus propagation model of susceptibility-infection-susceptibility based on a cellular automaton, as shown in figure 2;
the cellular automata CA is a simplified model and can simulate a dynamic system with internal interaction, and mainly comprises four major elements, namely a cell space C, a finite state set Q, a cell neighborhood V and a cell state conversion rule function delta, and is expressed as CA (C, Q, V, delta);
a network system is generally represented by a network graph G (N, E), where N is a set of all nodes in a network, E is a set of edges between all nodes in the network, and taking nodes in the network system as cells, the network including N nodes is a cellular automaton including N cells, N is a finite positive integer, and an SIS virus propagation model established according to four elements of the cellular automaton is:
cell space C: establishing a one-dimensional cellular space containing N cells at an initial moment;
finite state set Q: the states of the corresponding cells of the nodes are divided into a chromophil state and an infection state, which are respectively represented by 0 and 1, and a state set Q is {0, 1 }; si(t) is the state variable of the cell i at time t, Si(t) is equal to Q, then there is
Cell neighborhood V: the network adjacency matrix A (t) is the relation between each cell neighbor in the cell space, the neighbor of the cell i at the time t is the element set with all values of 1 in the ith row in A (t), alphaij＝1，αije.A (t) is the edge where there is a connection between cell i and cell j, and αii＝αjj＝0；
Cell state transition rule function δ: at each time t, the infected node infects neighboring nodes around the infected node with the probability of beta, and the infected node is recovered to be a healthy node with the probability of alpha, and the state transition function between the infected node and the healthy node is as follows:
in the formula, the upper horizontal line is an inverting operation, g is a state transition judgment function between an infected node and an susceptible node, and the state transition judgment function g between the infected node and the susceptible node is as follows:
wherein α represents a recovery rate, β represents an infection rate, γ is a random number between (0,1), and Sj(t) is the state variable of the cell j at the time t;
the proportion of infected nodes at the time t is I (t),
when the proportion of healthy nodes at the time t is S (t), I (t) and S (t) meet I (t) + S (t) ═ 1 at any time;
(2) giving a network graph G (N, E), wherein N represents a set of all nodes in a network, E represents a set of edges among all nodes in the network, initializing an adjacent matrix A (t) of the network at the time t, selecting m% of nodes as initial infection sources, and randomly selecting values of m and positions of the nodes;
(3) by utilizing a community structure discovery algorithm, a deletion order based on the whole network edge betweenness is obtained, and the method specifically comprises the following steps:
a. calculating the edge betweenness of each edge;
b. deleting the side with the largest edge betweenness;
c. recalculating edge betweenness of the rest edges in the network;
d. and (c) repeating the step (b) and the step (c) until the edge deletion sequence of the edge betweenness in the whole network is calculated.
(4) Determining the number of edge deletion to be k% by using a breadth-first search algorithm, wherein k is a finite positive integer;
in the process of temporary edge deletion, in order to ensure that the basic functions of the network are not influenced, the network functions are reflected through network connectivity, the change condition of the maximum connected subgraph scale in the network along with the increase of the number of temporary edge deletions is counted by using a breadth-first search algorithm, and the number k% of limited temporary edge deletions is further determined under the condition of meeting the requirement of given network connectivity;
(5) temporarily deleting an edge meeting the condition according to the edge betweenness deletion sequence obtained in the step (3);
(6) and (5) repeating the step until the temporary edge deletion ratio is k%.
In order to verify the beneficial effects of the invention, the inventor carries out simulation experiments, and the experimental conditions are as follows:
experiment 1
An actual small-world network containing 34 nodes, namely a Zachary empty hand club network and a medium-small-scale WS network containing 200 nodes are selected, based on the SIS virus propagation model in the embodiment, the propagation parameter recovery rate alpha and the infection rate beta in a simulation experiment are respectively set to be alpha 0.8 and beta 0.4, the initial infected node is 4% of the total randomly selected nodes, the temporary edge deletion number is less than 15%, and the temporary edge deletion number is determined on the premise of ensuring that the basic functions of the network are not influenced. In the simulation experiments, each curve value represents the average of 100 runs.
The network scale of fig. 3 is 34, that is, N is 34, the number of simulation steps is 25, the network scale of fig. 4 is 200, that is, N is 200, and the number of simulation steps is 50; fig. 3 and 4 show the variation trend of the proportion i (t) of the infected nodes in the network system under the control of different edge deletion methods as time t increases, and it can be known from the data analysis in the figure that:
(1) from the aspect of virus propagation speed, compared with a method without edge deletion, the method using random edge deletion and node degree edge deletion and the limited temporary edge deletion can slow down the propagation speed of the virus, but the effect of reducing the infection rate is most obvious;
(2) compared with other deletion methods, the invention has obvious advantages in inhibiting the spread of viruses from the scale of virus infection;
(3) whether the small-scale network comprising 34 nodes is shown in figure 3, or the small-scale network comprising 200 nodes is shown in figure 4, the invention can reduce the propagation speed of the virus, control the scale of the infected node, and verify the feasibility and the effectiveness of the method.
In order to examine the influence of the limited temporary edge deletion method on the network structure in the process of controlling virus propagation, the inventor performs the following experiments:
selecting the average path length L of the network structure property evaluation index to compare and analyze the performance change of the network structure under different edge deletion control methods, wherein the network average path length L is defined as the average value of the distance between any two nodes, and is:
in which N represents the number of nodes in the network, dijRepresenting the shortest path distance between a node i and a node j in the network; in order to avoid such divergence problem, the network average path length is further defined as an average value of distances between pairs of nodes where communication paths exist in the experiment, because the shortest path between two points may not exist, thereby resulting in an infinite average path length of the entire network.
With the increase of the number of edge deletion, the random edge deletion and the node degree edge deletion and the influence of the limited temporary edge deletion method on the average path length of the small-scale actual small-world characteristic network, as shown in fig. 5, compared with the random edge deletion and the effect of the node degree edge deletion method on the increase of the average path length of the network, the influence of the limited temporary edge deletion method on the increase of the average path length of the network is the most obvious.
With the increase of the number of edge deletion, the influence of three control methods of random edge deletion, node degree edge deletion and the limited temporary edge deletion method on the average path length of the WS network with a small scale is shown in fig. 6.
Considering the constraint of the edge deletion resources/cost, the experiment optimizes the temporary edge deletion resources, and how to optimize the limited edge deletion resource set so as to obtain the high performance of virus propagation control as much as possible is the aim of the temporary edge deletion resource optimization.
It is very important to maintain the connectivity of the network because edges are removed/managed from the network graph, which usually affects the degree of connection between the network transmission and the nodes, and even destroys the connectivity of the network, which is an important factor affecting the network structure. Experience and empirical research shows that many actual large-scale networks are not communicated, but a large communication slice often exists and contains nodes in a relative proportion in the whole network.
In the actual small-world network and WS network diagram, the maximum connected subgraph scale changes with the increase of the number of deleted edges, as shown in fig. 7 and 8, and as can be seen from data analysis in fig. 7 and 8, when the number of deleted edges is less than 15%, the invention can ensure that the connectivity of the network reaches at least 85%, so that not only can the propagation speed of the virus be well inhibited, but also the propagation scale of the virus be reduced, and the basic function of the network can be ensured not to be affected. Thus, controlling the number of temporary edges pruned by the connectivity of the network not only does the basic functionality of the network not suffer, but also takes into account the limited resources.
Claims (3)
1. A virus propagation control method based on limited temporary edge deletion is characterized by comprising the following steps:
(1) construction of a Virus propagation model
Establishing a susceptible-susceptible virus propagation model based on a cellular automaton;
(2) giving a network graph G (N, E), wherein N represents a set of all nodes in the network, E represents a set of edges among all nodes in the network, initializing an adjacent matrix A (t) of the network at the time t, selecting m% of nodes as initial infection sources, and m is a finite positive integer;
(3) by utilizing a community structure discovery algorithm, a deletion order based on the whole network edge betweenness is obtained, and the method specifically comprises the following steps:
a. calculating the edge betweenness of each edge;
b. deleting the side with the largest edge betweenness;
c. recalculating edge betweenness of the rest edges in the network;
d. repeating the step b and the step c until the edge deletion sequence of the edge betweenness in the whole network is calculated;
(4) determining the number of edge deletion to be k% by using a breadth-first search algorithm, wherein k is a finite positive integer;
in the process of temporary edge deletion, in order to ensure that the basic functions of the network are not influenced, the network functions are reflected through network connectivity, the change condition of the maximum connected subgraph scale in the network along with the increase of the number of temporary edge deletions is counted by using a breadth-first search algorithm, and the number k% of limited temporary edge deletions is further determined under the condition of meeting the requirement of given network connectivity;
(5) temporarily deleting an edge meeting the condition according to the edge betweenness deletion sequence obtained in the step (3);
(6) and (5) repeating the step until the temporary edge deletion ratio is k%.
2. The method of claim 1, wherein the virus propagation control method based on the limited temporary edge deletion comprises: in the step (1), the nodes in the network are used as the cells, the network comprising N nodes is the cellular automaton comprising N cells, N is a finite positive integer, and the susceptibility-virus propagation model established according to the four elements of the cellular automaton is as follows:
cell space C: establishing a one-dimensional cellular space containing N cells at an initial moment;
finite state set Q: the states of the corresponding cells of the nodes are divided into a chromophil state and an infection state, which are respectively represented by 0 and 1, and a state set Q is {0, 1 }; si(t) is the state variable of the cell i at time t, Si(t) is equal to Q, then there is
Cell neighborhood V: the network adjacency matrix A (t) is the relation between each cell neighbor in the cell space, the neighbor of the cell i at the time t is the element set with all values of 1 in the ith row in A (t), alphaij＝1，αije.A (t) is the edge where there is a connection between cell i and cell j, and αii＝αjj＝0；
Cell state transition rule function δ: at each time t, the infected node infects neighboring nodes around the infected node with a probability beta, and the infected node is recovered to be a healthy node with a probability alpha, and the state transition function between the infected node and the healthy node is as follows:
in the formula, the upper horizontal line is an inverting operation, g is a state transition judgment function between an infected node and an susceptible node, and the state transition judgment function g between the infected node and the susceptible node is as follows:
wherein α represents a recovery rate, β represents an infection rate, γ is a random number between (0,1), and Sj(t) is the state variable of the cell j at the time t;
the proportion of infected nodes at the time t is I (t),
when the proportion of healthy nodes at time t is s (t), at any time i (t) and s (t), i (t) + s (t) ═ 1 is satisfied.
3. The method of claim 1, wherein the virus propagation control method based on the limited temporary edge deletion comprises: the positions of m% nodes and the value of m are randomly selected.
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