CN108965287A - It is a kind of temporarily to delete the viral transmission control method on side based on limited - Google Patents
It is a kind of temporarily to delete the viral transmission control method on side based on limited Download PDFInfo
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Abstract
It is a kind of that viral transmission model is constructed based on the limited viral transmission control method for temporarily deleting side, the susceptible viral transmission model of susceptible-easy dye-is established based on cellular automata；Given network G (N, E) initializes the adjacency matrix A (t) of t moment network, chooses m% node as primary infection source；Using community structure find algorithm, obtain based on the whole network while betweenness when deleting sequence；Determine that deleting number of edges mesh is k% using breadth-first search, k is limited positive integer；It is interim to delete the side for meeting condition according to the sequence when betweenness is deleted；Previous step is repeated, until temporarily deleting side ratio is k%；The present invention has the advantages that simple and effective, significant decrease viral transmission speed and infection scale.
Description
Technical field
The invention belongs to field of computer technology, and in particular to a kind of based on the limited viral transmission control for temporarily deleting side
Method.
Background technique
With deepening continuously of studying Complex Networks Theory and develop, more and more researchers pay close attention to complex networks
Upper viral transmission dynamics, such as the viral transmission on computer network, rumour, the propagation of public opinion and biological net on social networks
The propagation etc. of disease in network.
In real life, each individual has the behavior gone after profits and advoided disadvantages, similarly for the node in network, it
Also can avoid and infect node contact by changing the network structure of oneself.Therefore, the topological structure of network is no longer quiet
It is only constant.
Be in the research of discipline roc et al. according to the relationship between side and important node, the side that be connected directly to important node or
Side of any two important node together between neighbor node is immunized.In the research of Shaw etc. and Gross et al. all
Think in the presence of having infection node in network, easily contaminating node can all select and infect node to disconnect, and reselect one
The healthy node of non-neighbours is attached thereto to make oneself to avoid the infected behavior to carry out self-protection.Risau-Gusman
Et al. also all have studied dissemination viral under a variety of reconnection methods.Later, Song Yurong et al. is confirmed in the course of the study
Reconnection method is to viral transmission inhibited.Cao Yulin et al. analyzes Song Yurong et al. method proposed,
Have also been proposed the reconnection method based on shortest path and node degree.However the optimization method of existing most of viral transmission controls,
It is all to be controlled using cut edge reconnection, but the cost that is spent of cut edge reconnection is than only carrying out deleting that side is big, realizes
Come also more complex, and does not account for limited resource constraints.
Summary of the invention
Technical problem to be solved by the present invention lies in providing, one kind is simple and effective, significantly reduces viral transmission speed and sense
Dye scale temporarily deletes the viral transmission control method on side based on limited.
Solving technical solution used by above-mentioned technical problem is: a kind of based on the limited viral transmission control for temporarily deleting side
Method comprises the steps of:
(1) viral transmission model is constructed
The susceptible viral transmission model of susceptible-easy dye-is established based on cellular automata；
(2) network G (N, E) is given, N indicates the set of all nodes in network, and E is indicated in network between all nodes
The set on side initializes the adjacency matrix A (t) of t moment network, chooses m% node as primary infection source, m for it is limited just
Integer；
(3) using community structure find algorithm, obtain based on the whole network while betweenness when deleting sequence；
(4) determine that deleting number of edges mesh is k% using breadth-first search, k is limited positive integer；
(5) sequence when betweenness is deleted obtained according to step (3), it is interim to delete the side for meeting condition；
(6) step (5) are repeated, until temporarily deleting side ratio is k%；
As a kind of perferred technical scheme, using the node in network as cellular in the step (1), then comprising N number of
The network of node is the cellular automata for including N number of cellular, and N is limited positive integer, is built according to four elements of cellular automata
Vertical susceptible-easy dye-susceptible virus propagation model are as follows:
Cellular space C: initial time foundation includes the one-dimensional cellular space of N number of cellular；
Finite state collection Q: the state that node corresponds to cellular is divided into easy dye state and Infection Status, and respectively with 0 and 1 table
Show, state set Q={ 0,1 }；SiIt (t) is state variable of the cellular i in t moment, Si(t) ∈ Q then has
Cellular neighborhood V: network adjacent matrix A (t) is the relationship in cellular space between each cellular neighbours, t moment member
The neighbours of born of the same parents i are the element set that all values of the i-th row are 1 in A (t), αij=1, αij∈ A (t) is between cellular i and cellular j
There are the side of connection, and αii=αjj=0；
Cellular state transformation rule function δ: it in each moment t, infects node and goes to infect surrounding neighbours' section with probability β
Point, while infected node also reverts to healthy node with probability α, the state infected between node and healthy node converts letter
Number are as follows:
In formula, upper horizontal line is inversion operation, and g is the state conversion discriminant function infected between node and susceptible node；
It is I (t) that t moment, which infects node proportion,T moment health node proportion is
S (t), then any moment I (t) and S (t) meet+S (t)=1 I (t).
As a kind of perferred technical scheme, the state between the infection node and susceptible node converts discriminant function
In formula, α indicates recovery rate, and β indicates that infection rate, γ take the random number between (0,1), SjIt (t) is cellular j in t
The state variable at quarter.
As a kind of perferred technical scheme, the position of m% node and the value of m are to randomly select.
Beneficial effects of the present invention are as follows:
Compared with prior art, the cost that the present invention is not only spent is small easy to accomplish, but also can reduce virus significantly
Spread speed and infection scale；The present invention is a kind of viral transmission control method unrelated with primary infection source, and interim
In the case where deleting finite population side, it can guarantee that the basic function of network system is unaffected.Simple and effective, cost of the invention
Expense is few, can be used as a kind of general optimal control method is applied to public sentiment Internet communication control, transportation network congestion is administered etc.
Field.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the limited viral transmission control method for temporarily deleting side.
Fig. 2 is dye susceptible in the present invention-easy-susceptible virus propagation model.
Fig. 3 is the simulation experiment result figure that the infection rate of small-scale real network changes over time.
Fig. 4 is the simulation experiment result figure that the infection rate of WS network changes over time.
Fig. 5 is the average path length of small-scale real network with the simulation experiment result figure for deleting side number of variations.
Fig. 6 is the average path length of WS network with the simulation experiment result figure for deleting side number of variations.
Fig. 7 is that the maximal connected subgraphs interior joint proportion of small-scale real network is real with the emulation for deleting side number of variations
Test result figure.
Fig. 8 is the maximal connected subgraphs interior joint proportion of WS network with the simulation experiment result for deleting side number of variations
Figure.
Specific embodiment
The present invention is described in more detail with reference to the accompanying drawings and examples, but the present invention is not limited to following embodiment party
Formula.
In Fig. 1, a kind of of the present embodiment temporarily deletes the viral transmission control method on side based on limited, by following steps group
At:
(1) the susceptible SIS viral transmission model of susceptible-easy dye-, such as Fig. 2 are established based on cellular automata；
Cellular automata CA is a kind of model of simplification, is that can simulate a kind of dynamical system with internal interaction
System, cellular automata CA mainly by cellular space C, finite state collection Q, cellular neighborhood V and cellular state transformation rule function δ this
Four big element compositions, are expressed as CA=(C, Q, V, δ)；
Network system usually uses network G (N, E) to indicate, N is the set of all nodes in network, and E is to own in network
The set on side between node, using the node in network system as cellular, then the network comprising N number of node includes as N number of member
The cellular automata of born of the same parents, N are limited positive integer, the SIS viral transmission model established according to four elements of cellular automata are as follows:
Cellular space C: initial time foundation includes the one-dimensional cellular space of N number of cellular；
Finite state collection Q: the state that node corresponds to cellular is divided into easy dye state and Infection Status, and respectively with 0 and 1 table
Show, state set Q={ 0,1 }；SiIt (t) is state variable of the cellular i in t moment, Si(t) ∈ Q then has
Cellular neighborhood V: network adjacent matrix A (t) is the relationship in cellular space between each cellular neighbours, t moment member
The neighbours of born of the same parents i are the element set that all values of the i-th row are 1 in A (t), αij=1, αij∈ A (t) is between cellular i and cellular j
There are the side of connection, and αii=αjj=0；
Cellular state transformation rule function δ: it in each moment t, infects node and goes to infect surrounding neighbours with the probability of β
Node, while infected node also reverts to healthy node with the probability of α, the state infected between node and healthy node turns
Exchange the letters number are as follows:
In formula, upper horizontal line is inversion operation, and g is the state conversion discriminant function infected between node and susceptible node, sense
The state contaminated between node and susceptible node converts discriminant function g are as follows:
In formula, α indicates recovery rate, and β indicates that infection rate, γ take the random number between (0,1), SjIt (t) is cellular j in t
The state variable at quarter；
It is I (t) that t moment, which infects node proportion,T moment health node proportion is
S (t), then any moment I (t) and S (t) meet+S (t)=1 I (t)；
(2) network G (N, E) is given, N indicates the set of all nodes in network, and E is indicated in network between all nodes
The set on side initializes the adjacency matrix A (t) of t moment network, chooses m% node as primary infection source, the value of m with
The position of node randomly selects；
(3) using community structure find algorithm, obtain based on the whole network while betweenness when deleting sequence, the specific steps are as follows:
A. calculate each while while betweenness；
B. it deletes when betweenness is maximum；
C. recalculate in network it is remaining while while betweenness；
D. step b and step c is repeated, until calculating in the whole network in betweenness when deleting until sequence.
(4) determine that deleting number of edges mesh is k% using breadth-first search, k is limited positive integer；
During temporarily deleting side, in order to guarantee that network basic function is unaffected, reflected by network connectivty
Network function, using breadth-first search statistics as interim number of edges mesh of deleting increases, maximal connected subgraphs scale in network
Situation of change, in the case where meeting given network-in-dialing demand, and then determine the limited number k% for temporarily deleting side；
(5) sequence when betweenness is deleted obtained according to step (3), it is interim to delete the side for meeting condition；
(6) step (5) are repeated, until temporarily deleting side ratio is k%.
In order to verify beneficial effects of the present invention, inventor has carried out emulation experiment, and experimental conditions are as follows:
Experiment 1
Choose comprising 34 nodes practical small-world network, that is, Zachary karate club's network and contain 200
The WS network of the middle and small scale of node is based on SIS viral transmission model in embodiment, propagation parameter recovery rate α in emulation experiment
It is α=0.8 with infection rate β difference value, β=0.4, primary infection node is randomly select total node number 4%, temporarily deletes side
Number is less than 15%, temporarily deletes number of edges mesh and determines under the premise of guaranteeing that network basic function is unaffected.In emulation experiment,
Every curve values all indicate the average value of 100 rounds of operation.
The network size of Fig. 3 is 34 i.e. N=34, and it is N=200 that the network size that step number be 25, Fig. 4 when emulation, which be 200, imitative
Step number is 50 when true；Fig. 3 and Fig. 4 shows the increase with time t, in the case where difference deletes the control of side method, feels in network system
The variation tendency for contaminating node proportion I (t), it was found from data analysis in figure:
(1) from the point of view of viral transmission speed, with without compared with deleting side method, using stochastic censored while and node degree delete while and this
The spread speed of virus can be slowed down by inventing limited side method of temporarily deleting, but the effect that the present invention reduces infection rate is the most aobvious
It writes；
(2) it from the point of view of viral infection scale, is deleted compared with the method for side with other, the present invention is bright to inhibiting the propagation of virus to have
Aobvious advantage；
(3) whether from the small scale network comprising 34 nodes, such as Fig. 3, or the middle and small scale comprising 200 nodes
Network, such as Fig. 4 demonstrate the party it can be seen that the present invention can reduce the spread speed and control infection node size of virus
The feasibility and validity of method.
Experiment 2
In order to investigate the present invention it is limited temporarily delete influence of side method during controlling viral transmission to network structure, hair
Bright people has carried out following experiment:
The average path length L of selection network structure properties evaluations index carrys out comparative analysis network structure and deletes side control in difference
Performance change under method processed, network average path length L are defined as the average value of the distance between any two node, i.e.,
Are as follows:
In formula, N indicates nodes number, dijIndicate the shortest path distance between nodes i and node j；
Since the shortest path between two o'clock may be not present, the average path length so as to cause whole network is infinity, in order to
This divergence problem is avoided the occurrence of, network average path length is further defined as in this experiment the node there are communication path
To the distance between average value.
Increase with number of edges purpose is deleted, stochastic censored while and node degree delete while and the present invention limited temporarily delete side method to small rule
The influence of the actual small world network average path length of mould, such as Fig. 5, with stochastic censored while node degree is deleted method
It is compared to the role of network average path length is increased, the limited side method of temporarily deleting of the present invention is to increase network average path
Effect length is the most obvious.
Increase with number of edges purpose is deleted, stochastic censored is when, node degree is deleted and the present invention is limited temporarily deletes three kinds of side method controls
The influence of the small-scale WS network average path length of method centering processed, such as Fig. 6, the limited side method of temporarily deleting of the present invention is with deleting
The increase of flash trimming number has a significant impact network average path length increase, and network average path length increase means network
Efficiency of transmission reduces, and illustrates that the limited side method of temporarily deleting of the present invention can effectively control viral transmission speed and propagate the reality of scale
Matter.
Experiment 3
In view of deleting the constraint of side resource/cost, this experiment is optimized to temporarily deleting side resource, how preferably limited
It deletes in resource set to obtain the target that viral transmission control high-performance is resource optimization when the present invention temporarily deletes as far as possible.
The some sides of deletion/control from network, this usually will affect between network transmission and node contiguity, even
The connectivity of network is destroyed, network connectivty is an important factor for influence on network structure, so keeping the connectivity of network is
It is very important.Experience and positive research show that many practical large scale networks are all disconnected, but often have one
A king-sized connection piece, it contains the node of significant proportion in whole network, and the present invention selects network structure property important
Index --- maximal connected subgraphs scale P includes interstitial content in that is, largest connected, as investigating according to preferably temporarily deleting
Line set.
Maximal connected subgraphs scale is with the deletion increased number of variation in side in practical small-world network and WS network
Situation, as shown in Figure 7 and Figure 8, data analysis can be seen that when deleting number of edges mesh less than 15% from Fig. 7 and Fig. 8, the present invention
It can guarantee that the connectivity of network is at least up to 85%, the spread speed of virus can not only be inhibited well in this way, reduce virus
Propagation scale, can also guarantee that the basic function of network is unaffected.Therefore, it is controlled by the connectivity of network and is temporarily deleted
The number on side, not only the basic function of network is unaffected, but also considers limited resources.
Claims (4)
1. a kind of based on the limited viral transmission control method for temporarily deleting side, it is characterised in that comprise the steps of:
(1) viral transmission model is constructed
The susceptible viral transmission model of susceptible-easy dye-is established based on cellular automata；
(2) network G (N, E) is given, N indicates the set of all nodes in network, side between all nodes in E expression network
Set initializes the adjacency matrix A (t) of t moment network, chooses m% node as primary infection source, m is limited positive integer；
(3) using community structure find algorithm, obtain based on the whole network while betweenness when deleting sequence；
(4) determine that deleting number of edges mesh is k% using breadth-first search, k is limited positive integer；
(5) sequence when betweenness is deleted obtained according to step (3), it is interim to delete the side for meeting condition；
(6) step (5) are repeated, until temporarily deleting side ratio is k%.
2. according to claim 1 based on the limited viral transmission control method for temporarily deleting side, it is characterised in that: described
Using the node in network as cellular in step (1), then the network comprising N number of node as includes that the cellular of N number of cellular is automatic
Machine, N are limited positive integer, susceptible-easy dye-susceptible virus propagation model established according to four elements of cellular automata are as follows:
Cellular space C: initial time foundation includes the one-dimensional cellular space of N number of cellular；
Finite state collection Q: the state that node corresponds to cellular is divided into easy dye state and Infection Status, and is indicated respectively with 0 and 1, shape
State collection Q={ 0,1 }；SiIt (t) is state variable of the cellular i in t moment, Si(t) ∈ Q then has
Cellular neighborhood V: network adjacent matrix A (t) is the relationship in cellular space between each cellular neighbours, t moment cellular i's
Neighbours are the element set that all values of the i-th row are 1 in A (t), αij=1, αij∈ A (t) exists between cellular i and cellular j
The side of connection, and αii=αjj=0；
Cellular state transformation rule function accounts for: in each moment t, infects node and goes to infect surrounding neighbor node with probability β,
Infected node also reverts to healthy node with probability α simultaneously, infects the state transition function between node and healthy node
Are as follows:
In formula, upper horizontal line is inversion operation, and g is the state conversion discriminant function infected between node and susceptible node；
It is I (t) that t moment, which infects node proportion,T moment health node proportion is S (t),
Then any moment I (t) and S (t) meet+S (t)=1 I (t).
3. according to claim 2 based on the limited viral transmission control method for temporarily deleting side, it is characterised in that: described
The state infected between node and susceptible node converts discriminant function
In formula, α indicates recovery rate, and β indicates that infection rate, γ take the random number between (0,1), SjIt (t) is shape of the cellular j in t moment
State variable.
4. according to claim 1 based on the limited viral transmission control method for temporarily deleting side, it is characterised in that: described
The position of m% node and the value of m are to randomly select.
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| CN113726802A (en) * | 2021-09-02 | 2021-11-30 | 中国人民解放军国防科技大学 | Network virus propagation analysis method, device, computer equipment and medium |
| CN114494643A (en) * | 2022-01-11 | 2022-05-13 | 西北工业大学 | Disease propagation control method based on network division |
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