CN117892225B - Virus propagation dynamics modeling method and device - Google Patents
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Abstract
The invention discloses a virus transmission dynamics modeling method and device, and relates to the technical field of temporary security. The method is used for solving the problem that the existing research cannot be applied to the dynamic scene change of the network structure caused by the space-time movement of the equipment. Comprising the following steps: determining that the unmanned aerial vehicle is positioned before and after emission according to the unmanned aerial vehicleIn the first placeProbability of not obtaining patch at moment, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofProbability of not being infected; if any unmanned aerial vehicle is confirmed to be infected, a patch is sent to the infected unmanned aerial vehicle, so that the infected unmanned aerial vehicle can clear viruses based on the patch; further, according to the unmanned plane in the firstAt the moment ofProbability of not obtaining patch, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofAnd unmanned plane is atThe probability of not being infected is obtained and the unmanned plane is at the firstA dynamic model based on Markov chains corresponding to the probability of the state at the moment.
Description
Technical Field
The invention relates to the technical field of clinical security, in particular to a method and a device for modeling virus propagation dynamics.
Background
With the breakthrough and innovation of internet of things (IoT, internet of Things) and wireless communication key technologies, clusters of Unmanned aerial vehicles (UAV, un-managed AERIAL VEHICLE) have gained considerable attention in both military and civilian fields, such as cargo delivery and low-altitude security facing future security systems. While wireless communication has made the drone swarm an indispensable tool in the physical world, the broad threat of malware attacks to network security has become widespread. Which often causes significant damage to the interconnected drones and increases the risk of sensitive data leakage. Constructing a mathematical model that accurately characterizes virus propagation against malware attacks has become an urgent and critical research topic for enhancing the security of unmanned clustered networks.
Currently, research into information physical systems has proposed a new multi-layered network framework to distinguish the interactions between the control theory space and the physical systems. At present, related problems have been studied at home and abroad, and the research results respectively comprise: a multi-layer network consisting of a logical network of interconnected telephone addresses and a geographic network of geographically adjacent telephone connections to study patch distribution policies in mobile telephones against virus attacks; a multi-layer network composed of a consensus network and a hidden network to maintain the stability of a collaboration system common in applications such as smart grids and traffic systems; a multi-layer network is used to study the effect of recovery coupling on the overall infrastructure system functions, including communication systems, power grids, and traffic systems. However, current research into multi-tier networks ignores spatio-temporal mobile devices caused by topology changes, which are not suitable for modeling unmanned clusters.
Disclosure of Invention
The embodiment of the invention provides a method and a device for modeling virus propagation dynamics, which are used for solving the problem that the existing research on a malicious software attack network cannot be suitable for a network structure dynamic change scene caused by space-time movement of equipment.
The embodiment of the invention provides a virus propagation dynamics modeling method, which comprises the following steps:
according to unmanned plane in the first The probability of the state where the moment is located and the probability transition tree of the physical state are obtained from the unmanned aerial vehicle at the first placeProbability of the state at the moment; wherein the state comprises patch installation and easy infectionPatch is not installed and is easy to be infectedAnd installed and infected with patch; Before the launching, according to the unmanned plane beingIs in the unmanned planeDetermining that the unmanned aerial vehicle is in the probability of the supervisory layer, the adjacency matrix of the supervisory layer and the patch distribution rateProbability of not obtaining a patch;
after the launching, at least one unmanned aerial vehicle flies from the first area to the second area, and the unmanned aerial vehicle positioned in the first area is positioned according to the probability of leaving to execute the task Probability of not being infected by the same area, unmanned aerial vehicle located in first area is inProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedThe probability of being not infected by the same area and the task layer normalized adjacency matrix sequentially determine that unmanned aerial vehicles belonging to the first area are in the first areaAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofProbability of not being infected;
If any unmanned aerial vehicle is confirmed to be infected, a patch is sent to the infected unmanned aerial vehicle, so that the infected unmanned aerial vehicle can clear viruses based on the patch;
according to the unmanned aerial vehicle is in Probability of not obtaining patch, unmanned aerial vehicle is inDue to the probability of virus removal by installing patches, the unmanned aerial vehicle is inProbability of losing immunity, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofThe probability of not being infected is obtained and the unmanned plane is at the firstA dynamic model based on Markov chains corresponding to the probability of the state at the moment.
Preferably, the dynamic model based on markov chains is as follows:
wherein, Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Indicating that the unmanned aerial vehicle is inThe probability of losing the immunity of the human body,Representation of belonging to a regionUnmanned aerial vehicle of (2) is in the firstAt the moment ofThe probability of not being infected is that,Indicating that the unmanned aerial vehicle is inProbability of not obtaining a patch; Representation unmanned aerial vehicle In the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Indicating that the unmanned aerial vehicle is inBecause of the probability that the patch is installed to clear the virus,Representation of belonging to a regionUnmanned aerial vehicle of (2) is in the firstAt the moment ofThe probability of not being infected is that,Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a probability of (2).
Preferably, the unmanned aerial vehicle located in the second area is located inThe probability of not being infected by the same area is expressed by the following formula:
the unmanned aerial vehicle located in the second area is located in The probability of not being infected by the same area is expressed by the following formula:
wherein, Indicating that the drone located in the second zone is inThe probability of not being infected by the same area,Representation of belonging to a regionInner unmanned plane is inIs used for the density of the (c) in the (c),，Representation unmanned aerial vehicleIn the first placeAt the moment ofIn the probability that the probability of a given event,Representing the inter-layer bordering of the task layer and the supervisory layer,Indicating that the unmanned aerial vehicle is inThe average probability of being infected without a defense strategy,The representation is located in the regionIs at unmanned aerial vehicle of (1)Randomly selecting and selecting a slave regionProbability of the flying drone not being infected after communication,Represent the firstFrom time of day regionFly to the areaIs provided for the number of unmanned aerial vehicles desired,Indicating that the drone located in the second zone is inThe probability of not being infected by the same area,Indicating that the unmanned aerial vehicle is inWith the average probability of being infected in the case of a defensive strategy,Representing the number of regions of the task layer.
Preferably, the unmanned aerial vehicle belonging to the first area is at the first positionAt the moment ofThe probability of not being infected is expressed by the following formula:
the unmanned aerial vehicle belonging to the first area is at the first At the moment ofThe probability of not being infected is expressed by the following formula:
wherein, Indicating that the unmanned aerial vehicle belonging to the first area is at the firstAt the moment ofThe probability of not being infected is that,The probability of leaving to perform a task is represented,Indicating that the unmanned aerial vehicle located in the first area is locatedThe probability of not being infected by the same area,Representing the task layer normalized adjacency matrix,Indicating that the drone located in the second zone is inProbability of not being infected by the same area; Indicating that the unmanned aerial vehicle belonging to the first area is at the first At the moment ofThe probability of not being infected is that,Indicating that the unmanned aerial vehicle located in the first area is locatedThe probability of not being infected by the same area,Indicating that the drone located in the second zone is inProbability of not being infected by the same area.
Preferably, the unmanned aerial vehicle is inThe probability of not obtaining a patch from a neighbor drone is as follows:
wherein, Representation unmanned aerial vehicleIn the first placeThe probability of installing the patch at the moment,，Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),The patch distribution rate is represented by the number of patches,Representing the adjacency matrix of the supervisory layer,Indicating that the unmanned aerial vehicle is inThe probability that a patch is not obtained from a neighbor drone,Representing the number of drones.
Preferably, the unmanned aerial vehicle is obtained on the basis of the physical state probability transition treeThe probability of the state at the moment is as follows:
wherein, Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeThe probability that the moment is in PS,Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),。
Preferably, the unmanned plane is at the first positionThe probability of the state where the moment is located and the probability transition tree of the physical state are obtained from the unmanned aerial vehicle at the first placeBefore the probability of the state at the moment, the method further comprises:
Constructing a multi-layer network model consisting of a supervision layer and a task layer, wherein the supervision layer comprises a plurality of first nodes which are unmanned planes, and the connection edges among the first nodes represent communication connection in a satellite or cellular network;
the task layer comprises a plurality of second nodes which represent areas where the unmanned aerial vehicle can communicate with each other, and the connecting edges among the plurality of second nodes represent the flight route of the unmanned aerial vehicle.
The embodiment of the invention provides a virus propagation dynamics modeling device, which comprises:
a first determining unit, configured to determine that the unmanned aerial vehicle is at the first position The probability of the state where the moment is located and the probability transition tree of the physical state are obtained from the unmanned aerial vehicle at the first placeProbability of the state at the moment; wherein the state comprises patch installation and easy infectionPatch is not installed and is easy to be infectedAnd installed and infected with patch; Before the launching, according to the unmanned plane beingIs in the unmanned planeDetermining that the unmanned aerial vehicle is in the probability of the supervisory layer, the adjacency matrix of the supervisory layer and the patch distribution rateProbability of not obtaining a patch;
A second determining unit for, after transmission, enabling at least one unmanned aerial vehicle to fly from the first area to the second area, wherein the unmanned aerial vehicle in the first area is located according to the probability of leaving the first area to execute the task Probability of not being infected by the same area, unmanned aerial vehicle located in first area is inProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedThe probability of being not infected by the same area and the task layer normalized adjacency matrix sequentially determine that unmanned aerial vehicles belonging to the first area are in the first areaAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first areaAt the moment ofProbability of not being infected;
a sending unit, configured to send a patch to an infected unmanned aerial vehicle if any one unmanned aerial vehicle is confirmed to be infected, so that the infected unmanned aerial vehicle performs virus removal based on the patch;
obtaining a unit for according to the unmanned aerial vehicle being in Probability of not obtaining patch, unmanned aerial vehicle is inDue to the probability of virus removal by installing patches, the unmanned aerial vehicle is inProbability of losing immunity, unmanned aerial vehicle belonging to first area is inIn the first placeProbability of not being infected at the moment and that unmanned aerial vehicle belonging to first area is inIn the first placeThe probability of not being infected at the moment is obtained and the unmanned plane is at the first positionA dynamic model based on Markov chains corresponding to the probability of the state at the moment.
An embodiment of the present invention provides a computer device, where the computer device includes a memory and a processor, where the memory stores a computer program, and where the computer program when executed by the processor causes the processor to execute any one of the foregoing virus propagation dynamics modeling methods.
An embodiment of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform any one of the above-described virus propagation dynamics modeling methods.
The embodiment of the invention provides a method and a device for modeling virus propagation dynamics, wherein the method comprises the following steps: according to unmanned plane in the firstThe probability of the state where the moment is located and the probability transition tree of the physical state are obtained from the unmanned aerial vehicle at the first placeProbability of the state at the moment; wherein the state comprises patch installation and easy infectionPatch is not installed and is easy to be infectedAnd installed and infected with patch; Before the launching, according to the unmanned plane beingIs in the unmanned planeDetermining that the unmanned aerial vehicle is in the probability of the supervisory layer, the adjacency matrix of the supervisory layer and the patch distribution rateProbability of not obtaining a patch; after the launching, at least one unmanned aerial vehicle flies from the first area to the second area, and the unmanned aerial vehicle positioned in the first area is positioned according to the probability of leaving to execute the taskProbability of not being infected by the same area, unmanned aerial vehicle located in first area is inProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedThe probability of being not infected by the same area and the task layer normalized adjacency matrix sequentially determine that unmanned aerial vehicles belonging to the first area are in the first areaAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofProbability of not being infected; if any unmanned aerial vehicle is confirmed to be infected, a patch is sent to the infected unmanned aerial vehicle, so that the infected unmanned aerial vehicle can clear viruses based on the patch; according to the unmanned aerial vehicle is inProbability of not obtaining patch, unmanned aerial vehicle is inDue to the probability of virus removal by installing patches, the unmanned aerial vehicle is inProbability of losing immunity, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofThe probability of not being infected is obtained and the unmanned plane is at the firstA dynamic model based on Markov chains corresponding to the probability of the state at the moment. The method is based on a multi-layer network to describe virus transmission in the unmanned cluster, provides theoretical support for unmanned cluster information security and defense, and comprises a task layer and a supervision layer, wherein the task layer is used for describing the transmission process of malicious software and patches; the nodes of the supervision layer represent unmanned aerial vehicles, the edges represent communication supporting patch distribution among the unmanned aerial vehicles, the task layer is constructed into a multi-region structure, the nodes represent different regions of the unmanned aerial vehicles for executing tasks, the edges represent flight routes of the unmanned aerial vehicles among the regions, and the malicious software diffusion in unmanned clusters of different regions, which are flown by the unmanned aerial vehicles under the driving of the tasks, is captured by combining various conditions of the unmanned aerial vehicles before and after the transmission and the infection of the self-checking unmanned aerial vehicles by viruses and the like, and on the basis, a dynamic model based on a microcosmic Markov chain is established for describing the dynamic characteristics of the malicious software propagation and patch distribution. The method can solve the problem that the existing research cannot be applied to the dynamic scene change of the network structure caused by the space-time movement of the equipment.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for modeling virus propagation dynamics according to an embodiment of the present invention;
Fig. 2 is a schematic view of a scene of an unmanned aerial vehicle flying to different areas according to an embodiment of the present invention;
Fig. 3 is a schematic view of a scenario of a malware attack unmanned plane provided by an embodiment of the present invention;
fig. 4 is a schematic diagram of three state transition scenarios of an unmanned aerial vehicle according to an embodiment of the present invention;
Fig. 5 is a schematic diagram of a malware attack unmanned plane and a patch distribution scenario provided by an embodiment of the present invention;
FIG. 6 is a schematic diagram of a multi-layer network according to an embodiment of the present invention;
Fig. 7 is a schematic diagram of a physical state probability transition tree structure of an unmanned aerial vehicle according to an embodiment of the present invention;
Fig. 8 is a schematic structural diagram of a virus propagation dynamics modeling apparatus according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
FIG. 1 is a schematic flow chart of a method for modeling virus propagation dynamics according to an embodiment of the present invention; as shown in fig. 1, the method for modeling virus propagation dynamics provided by the embodiment of the invention mainly includes the following steps:
step 101, according to the unmanned aerial vehicle in the first place The probability of the state where the moment is located and the probability transition tree of the physical state are obtained from the unmanned aerial vehicle at the first placeProbability of the state at the moment; wherein the state comprises patch installation and easy infection(PATCHED AND susceptible) Patch is not installed and is susceptible to infection(Unpatched and susceptible) and installed and infected with patch（patched and infected）；
Step 102, before transmitting, according to the unmanned aerial vehicle being inIs in the unmanned planeDetermining that the unmanned aerial vehicle is in the probability of the supervisory layer, the adjacency matrix of the supervisory layer and the patch distribution rateProbability of not obtaining a patch;
step 103, after the launching, at least one unmanned aerial vehicle flies from the first area to the second area, and according to the probability of leaving the unmanned aerial vehicle in the first area to execute the task, the unmanned aerial vehicle is in Probability of not being infected by the same area, unmanned aerial vehicle located in first area is inProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedThe probability of being not infected by the same area and the task layer normalized adjacency matrix sequentially determine that unmanned aerial vehicles belonging to the first area are in the first areaAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofProbability of not being infected;
104, if any unmanned aerial vehicle is confirmed to be infected, sending a patch to the infected unmanned aerial vehicle so that the infected unmanned aerial vehicle can remove viruses based on the patch;
step 105, according to the unmanned aerial vehicle being in Probability of not obtaining patch, unmanned aerial vehicle is inDue to the probability of virus removal by installing patches, the unmanned aerial vehicle is inProbability of losing immunity, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofThe probability of not being infected is obtained and the unmanned plane is at the firstA dynamic model based on Markov chains corresponding to the probability of the state at the moment.
Before describing the method provided by the embodiment of the invention, parameters involved in the method are described with reference to fig. 2-5, and a multi-layer network model applied by the method is described with reference to fig. 6.
In practical application, when the unmanned aerial vehicle flies from the area to which the unmanned aerial vehicle belongs to different areas, the unmanned aerial vehicle flies at a set speedStarting from the area (first area) to which the unmanned aerial vehicle belongs, going to a destination (second area), and after the unmanned aerial vehicle arrives at the ground station of the destination, the unmanned aerial vehicle can transmit control signals and data at the ground station of the destination; and returning the unmanned aerial vehicle to the area after the destination finishes the task, and waiting for the next task. With unmanned aerial vehicle in figure 2For example, unmanned aerial vehicleProceeding from the area A to the target area C, while the unmanned plane isAfter reaching the area C, unmanned aerial vehicleGround station needing to enter area C to transmit control signals and data, and when unmanned planeAfter the region C completes the task, it returns from the region C to the belonging region a, waiting for the next task.
When an attacker attacks a drone cluster before the drone takes off, a typical strategy is to initiate malware attacks from a particular drone, these infected drones, after flying to different areas, when the infected drone arrives at the destination, it establishes a connection with other drones located in the same area through the ground station of the destination. At this time, the susceptible unmanned aerial vehicle which is located in the same distinction as the infected unmanned aerial vehicle may be implanted with malware with a certain probability, and if there is no defense strategy, the probability of being implanted with malware may be set to be(Design)）。
As shown in fig. 3, in order to distinguish the state of the drone in fig. 3, the drone is here inThe mark is triangle-shaped, and unmanned aerial vehicle is inThe marks are circular. Malicious software is implanted into the unmanned aerial vehicle No. 6 included in the area B and the unmanned aerial vehicle No. 8 included in the area C, and when the unmanned aerial vehicle 6 flies to the areaWhen the unmanned aerial vehicle 8 flies to the area B, the unmanned aerial vehicle 6 spreads the malicious software to the unmanned aerial vehicle 7 and the unmanned aerial vehicle 2, and the unmanned aerial vehicle 8 spreads the malicious software to the unmanned aerial vehicle 3, the unmanned aerial vehicle 5 and the unmanned aerial vehicle 9. After the task is completed, all unmanned aerial vehicles return to the area where the unmanned aerial vehicles are located. After a period of time, all drones in the system may become infected.
As shown in fig. 4, in the embodiment of the present invention, in order to mitigate a malware attack in an unmanned aerial vehicle cluster, and protect information security of the unmanned aerial vehicle cluster, a patch policy is adopted. Specifically, after the central server detects the abnormal state, the patch is timely distributed to the unmanned aerial vehicle corresponding to the abnormal state through the centralized patch distribution part. The unmanned aerial vehicle receiving the patch propagates the patch to other unmanned aerial vehicles through the distributed patch distribution part with a certain probability according to the connection condition of the satellite or the cellular network where the unmanned aerial vehicle is located. Specifically, for a unmanned aerial vehicle to which no patch is installed, when the unmanned aerial vehicle has been infected, it obtains the patch from the central server in time through the centralized patch distribution section, and the unmanned aerial vehicle is in the state ofI.e. the unmanned aerial vehicle is in. A frame of susceptible unmanned aerial vehicle without patches, namely unmanned aerial vehicle is inThe unmanned aerial vehicle is atThe probability of obtaining a patch from an adjacent one of the patched drones by the distributed patch distribution portion isThe status of the adjacent unmanned aerial vehicle is that、、Any one of the unmanned aerial vehicle with a certain probabilityPutting it inTransferred to be inIs a process of (2). Meanwhile, the patch does not provide permanent protection, and the patch may fail to the new malware with a certain probability. When the patch fails, the unmanned aerial vehicle is positioned atTransferred to be inThe probability of (2) is. Furthermore, considering that the patch is not fully immune to advanced persistent threats or multi-platform viruses, i.e. the risk of the patch-installed drone being infected by malware will be reduced, but not provide full protection. The unmanned aerial vehicle is atOr the unmanned aerial vehicle is inIs in contact with a unmanned planeAfter a single communication, the infection rates are respectivelyAnd. Here, theWherein. Meanwhile, as the patch can remove the malicious software corresponding to the virus, the unmanned aerial vehicle is currently inWill be transferred back to be in the state after a period of time. At the rate of malware elimination. In fig. 4, in order to distinguish the status of the drone, the drone is here inThe mark is triangle-shaped, and unmanned aerial vehicle is inMarked as a square, the drone is atThe marks are circular.
As shown in fig. 5, the unmanned aerial vehicle No. 6 and the unmanned aerial vehicle No. 8 receive the patch from the central server through the centralized patch distribution part once they are infected, and the unmanned aerial vehicle No. 6 and the unmanned aerial vehicle No. 8 probability before the next transmission(Design)) And distributing the patch to the unmanned aerial vehicle No. 4, the unmanned aerial vehicle No. 5, the unmanned aerial vehicle No. 7 and the unmanned aerial vehicle No. 9. If the patch provides complete protection) When the unmanned aerial vehicle 6 flies to the area C, the unmanned aerial vehicle 6 with probability(Design)) Spreading the malicious software to the unmanned aerial vehicle 2; when the drone 8 flies to zone B, the drone 8 probabilities(Design)) The malware is propagated to the drone 3. Meanwhile, under the action of the patch, malicious software codes in the unmanned aerial vehicle 6 and the unmanned aerial vehicle 8 are cleared) Its state is transferred back to being in. After the task is completed, all unmanned aerial vehicles return to the area where the unmanned aerial vehicles are located. After a period of time, all of the drones in the system may not be infected.
Therefore, in this application scenario, the initialization parameters of the model provided by the embodiment of the present invention include the following:
: probability of infection, indicating that the unmanned aerial vehicle is in Is in contact with an unmanned planeProbability of infected virus after communication.
: Recovery rate, indicating that the unmanned aerial vehicle is inDue to the probability that the installed patch is cleared of viruses.
: Patch distribution rate, which means that due to the limitation of network bandwidth, one unmanned aerial vehicle is inIs distributed by distributed patches from a single unmanned plane in the same areaOr alternativelyThe probability of obtaining the patch.
: Indicating that the unmanned aerial vehicle is inProbability of losing immunity.
: Representing the probability of the drone leaving the area to perform a task.
: Indicating the level of immunity provided by the patch.
FIG. 6 provides a layer of supervision for an embodiment of the inventionAnd task layerThe multi-layer network model is formed, and the competition process between the malicious software attack and the patch distribution can be clearly shown through the multi-layer network model. At the supervision layerWherein, the real points represent unmanned aerial vehicles, and the connection between the real points represents communication connection in satellite or cellular network; at the task layerIn the middle, the empty circles represent areas consisting of a plurality of unmanned aerial vehicles, and the connecting lines among the areas represent the flight routes of the unmanned aerial vehicles.
Specifically, the multi-layer network model is represented by formula (1):
（1）
wherein, Representing the layers of the multi-layer network,Representing a set of networks,Representing inter-layer bordering.
Supervision layerExpressed by formula (2):
（2）
wherein, ，Representing a set of first nodes, at a supervisory layerThe first node in the network is an unmanned aerial vehicle,，Representing the set of first edges, at the supervisory layerThe first side of (a) represents a communication connection in a satellite or cellular network.
Supervision layerThe total number of the first nodes isM represents the number of regions (second nodes), supervisory layerIs expressed as an adjacency matrix of (2)Wherein if the nodeSum nodeIf there is a connection, then=1, Otherwise,=0。
Task layerIs expressed by the following formula:
（3）
wherein, ，Representing a set of second nodes, at task levelThe second node in (c) represents an area where the drones can communicate with each other,，Representing the second set of edges, at the task levelThe second side of (c) represents the flight path of the drone between the various zones.
Task layerIs expressed as an adjacency matrix of (2)Task layerNormalized adjacency matrix of (2) is。
Further, supervisory layerAnd task layerThe interrelationship between is represented by an incidence matrix:
（4）
wherein,
In practical application, the unmanned aerial vehicle is driven by a flight task and is arranged on a task layerAt a rate of unmanned aerial vehicleSlave regionLaunching, unmanned aerial vehicle flies to the regionIs defined by the task layerNormalized adjacency matrix of (2)And (5) determining.
In the embodiment of the invention, the task layer is constructed into a multi-area structure to depict that unmanned aerial vehicles driven by the spreading tasks of the malicious software fly in different areas, and the supervision layer is established into a heterogeneous network to support patch distribution.
For unmanned clusters, discrete dynamic operations on a multi-layer network model can be derived with the help of microscopic Markov chains, which can be represented by a physical state probability transition tree. The physical state probability transition tree characterizes all possible transitions in the unmanned plane state in the model. As shown in fig. 7, a susceptible unmanned aerial vehicle without a patch installed, i.e. the unmanned aerial vehicle is inIt obtains patches from adjacent patched drones through a distributed patch distribution portion, where the status of adjacent patched drones may be asMay also beIn this case, if the drone does not obtain a patch from an adjacent drone that has a patch already installed, the drone will still be inI.e. probability of unmanned aerial vehiclePutting it inIs turned to be in; At the same time, due to new malware, the drone is atAnd lose immunity, unmanned aerial vehicle is at a rateWill be inIs transferred again to be in. After being transmitted, belong to the areaIs at unmanned aerial vehicle of (1)The probability of being infected during the execution of a task isOr belong to a regionIs at unmanned aerial vehicle of (1)The probability of being infected during the execution of a task is. In the process of executing the task, when the unmanned aerial vehicle is infected, the unmanned aerial vehicle timely obtains the patch through the centralized patch distribution part, and the state of the unmanned aerial vehicle is thatI.e. the unmanned aerial vehicle is in. In addition, other unmanned aerial vehicles are in the process of being provided by anti-malwareWhen it eliminates malware at a rate of。
It should be noted that, in the virus propagation dynamics modeling method provided by the embodiment of the present invention, the execution body is a central server, the central server may communicate with a plurality of unmanned aerial vehicles at a task layer through a certain transmission protocol, and in this process, patch distribution may be performed through a centralized patch distribution part; before the unmanned aerial vehicles transmit, a first transmission protocol between the unmanned aerial vehicles is disconnected, a second transmission protocol provided by the central server is connected, and the unmanned aerial vehicles distribute patches through a distributed patch distribution part through the second transmission protocol. After the unmanned aerial vehicle transmits, the second transmission protocol is disconnected, the first transmission protocol is connected, a plurality of unmanned aerial vehicles belonging to the same area can be connected through the first transmission protocol, and the connection can realize the propagation of malicious software; further, when a certain unmanned aerial vehicle is infected with a virus corresponding to malware, a central server in single-line communication with the unmanned aerial vehicle may directly distribute patches to the unmanned aerial vehicle through the centralized patch distribution section.
In step 101, a unmanned aerial vehicle is at the first positionThree physical states may exist at a moment, the three states being respectively、And. The unmanned aerial vehicle is atIndicating that the unmanned aerial vehicle is in the condition of being provided with patches and easy to infect, and the unmanned aerial vehicle is inIndicating that the unmanned aerial vehicle is in a state of not installing patches and is susceptible, and the unmanned aerial vehicle is inIndicating that the drone is in the patch installed and infected.
Further, the method comprises the steps of,Representation unmanned aerial vehicleIn the first placeAt the moment ofAnd the probabilities of the three states can be expressed by the following formula:
（5）
wherein, Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a probability of (2).
In practical application, if a unmanned aerial vehicle is knownIn the first placeThe probability of the state of the moment can be deducedIn the first placeAt the moment ofThese three state probabilities can be expressed by the following formulas:
（6）
（7）
（8）
wherein, Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toProbability of (2)。
In practical application, the probability transition tree according to the physical state can be obtainedThe expression of (2) is as follows:
（9-1）
（9-2）
（9-3）
（9-4）
（9-5）
（9-6）
（9-7）
（9-8）
（9-9）
wherein, Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeFrom time to time stateConversion toIs a function of the probability of (1),Representation of belonging to a regionUnmanned aerial vehicle of (2) is in the firstAt the moment ofThe probability of not being infected is that,Indicating that the unmanned aerial vehicle is inProbability of not obtaining a patch; Indicating that the unmanned aerial vehicle is in Because of the probability that the patch is installed to clear the virus,Indicating that the unmanned aerial vehicle is inProbability of losing immunity; representation of belonging to a region Unmanned aerial vehicle of (2) is in the firstAt the moment ofProbability of not being infected.
In step 102, the drones are connected by a second transmission protocol between the drones before transmitting, at which time the drones may get the patch from other drones that have obtained the patch, a process that distributes the patch for distribution. If the unmanned aerial vehicle is inWhether it was in from the drone before the launchOr alternativelyThe probability of obtaining a patch at a neighbor of (2) is determined by the topology of the supervisory layer and the probability of whether the neighbor has installed the patch, which may also be referred to as the drone being inThe probability of not obtaining a patch is specifically as follows:
（10）
wherein, Representation unmanned aerial vehicleIn the first placeThe probability of installing the patch at the moment,，Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),The patch distribution rate is represented by the number of patches,Representing the adjacency matrix of the supervisory layer,Indicating that the unmanned aerial vehicle is inThe probability of a patch not being obtained from a neighbor.
Further, before the unmanned aerial vehicle flies from the area to other areas, the first determination is neededThe expected number of drones flying from the first area to the second area at a time is as follows:
（11）
wherein, Representing the Kronecker function ifElement(s)Otherwise。The probability of leaving to perform a task is represented,Representing task layersMiddle regionThe number of unmanned aerial vehicles involved in the process,Representing task layersMiddle regionThe number of unmanned aerial vehicles involved in the process,Representing task layersIs provided for the normalized adjacency matrix of (2).
The above-mentionedIndicating the probability of leaving to perform a task, where leaving refers to the unmanned aerial vehicle from the area to which it belongsLeaving, the unmanned aerial vehicle may be located in any one area, so specific area names are not limited herein. In the above formula, the first term on the right of the equal sign indicates that the stay in the regionThe second item on the right of the equal sign indicates the slave regionFlying to the areaThe number of unmanned aerial vehicles.
In the embodiment of the invention, the first area represents the area where the unmanned aerial vehicle is located before being launched, and the second area represents the area where the unmanned aerial vehicle flies after being launched, in the example, the areaRepresenting the area of the unmanned aerial vehicle before transmittingIndicating the area to which the drone flies after launching.
Further, the first calculation is needed before transmissionThe moment belongs to the areaIs at unmanned aerial vehicle of (1)And unmanned plane is atThe probability of not being infected is expressed specifically as:
（12-1）
（12-2）
wherein, Representation of belonging to a regionIs at unmanned aerial vehicle of (1)The probability of not being infected by the same area,Representation of belonging to a regionInner unmanned plane is inIs used for the density of the (c) in the (c),，Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representing the inter-layer bordering of the task layer and the supervisory layer,Indicating that the unmanned aerial vehicle is inThe average probability of being infected without a defense strategy,The representation is located in the regionIs at unmanned aerial vehicle of (1)Randomly selecting and selecting a slave regionThe probability of remaining vulnerable to infection after the flying drone communicates,Represent the firstFrom time of day regionFly to the areaIs provided for the number of unmanned aerial vehicles desired,The representation is located in the regionIs at unmanned aerial vehicle of (1)The probability of not being infected by the same area,Indicating that the unmanned aerial vehicle is inWith the average probability of being infected in the case of a defensive strategy,Representing the number of regions of the task layer.
Further, the method comprises the steps of,The representation is located in the regionIs at unmanned aerial vehicle of (1)Time random selectionFrame slave regionProbability of remaining susceptible after flying drone and communicating therewith.
In the embodiment of the invention, the first area represents the area where the unmanned aerial vehicle is located before being launched, and the second area represents the area where the unmanned aerial vehicle flies after being launched, in the example, the areaRepresenting the area of the unmanned aerial vehicle before transmittingIndicating the area to which the drone flies after launching.
Further, since not all the unmanned aerial vehicles fly from the first area to the second area after the unmanned aerial vehicle is launched, the unmanned aerial vehicle left in the first area is called as an unmanned aerial vehicle belonging to the first area and located in the first area after the unmanned aerial vehicle is launched, and also can be simply called as an unmanned aerial vehicle located in the first area; for the sake of distinction, a drone flying from a first area to a second area is referred to as a drone belonging to the first area and located in the second area after the launch, and may also be referred to as a drone located in the second area for short.
In step 103, after the unmanned aerial vehicle transmits, each area has at least one unmanned opportunity to fly from the area where the unmanned aerial vehicle is located to another area, and accordingly, each area may have one unmanned opportunity to stay in the area where the unmanned aerial vehicle is located. In practical application, in the flight process, communication connection is established between unmanned aerial vehicles in the same area, so that virus may be spread.
In the embodiment of the invention, the unmanned aerial vehicle in the first area is positioned according to the probability of leaving to execute the taskProbability of not being infected by the same areaThe unmanned aerial vehicle located in the first area is located inProbability of not being infected by the same areaThe unmanned aerial vehicle located in the second area is located inProbability of not being infected by the same areaThe unmanned aerial vehicle located in the second area is located inProbability of not being infected by the same areaNormalized adjacency matrix with task layerThe unmanned aerial vehicle belonging to the first area can be sequentially determined to be in the first areaAt the moment ofProbability of not being infectedAnd the unmanned aerial vehicle belonging to the first area is in the first areaAt the moment ofProbability of not being infectedThe method is specifically as follows:
（13）
（14）
wherein, Indicating that the unmanned aerial vehicle belonging to the first area is at the firstAt the moment ofThe probability of not being infected is that,The probability of leaving to perform a task is represented,Indicating that the unmanned aerial vehicle located in the first area is locatedThe probability of not being infected by the same area,Representing the task layer normalized adjacency matrix,Indicating that the drone located in the second zone is inProbability of not being infected by the same area; Indicating that the unmanned aerial vehicle belonging to the first area is at the first At the moment ofThe probability of not being infected is that,Indicating that the unmanned aerial vehicle located in the first area is locatedThe probability of not being infected by the same area,Indicating that the drone located in the second zone is inProbability of not being infected by the same area.
It should be noted that the number of the substrates,Indicating that the drone located in the second zone is inThe probability of not being infected by the same area, which can be expressed by the following formula:
（15-1）
Indicating that the drone located in the second zone is in Probability of not being infected by the same area, wherein it can be expressed by the following formula:
（15-2）
in step 104, if the drone is in any state and is located in any area after the transmitting, after the central server located in the background or the satellite determines that the drone is infected, the central server sends a patch to the infected drone, so that the infected drone clears the infected virus according to the received patch.
In step 105, after the unmanned aerial vehicle is navigated back, a dynamic model between the malware attack and the patch distribution is deduced through a microscopic markov chain method according to the physical state probability transition tree.
In particular according to the unmanned aerial vehicle being inIn the probability of not obtaining a patch, the unmanned aerial vehicle is inDue to the probability of virus removal by installing patches, the unmanned aerial vehicle is inProbability of losing immunity, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofProbability of not being infected, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofThe probability of not being infected results in a dynamic model based on Markov chains, which is on the first hand with the droneThe probability of the state at the moment corresponds to the following specific:
（16）
（17）
（18）
wherein, Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Indicating that the unmanned aerial vehicle is inThe probability of losing the immunity of the human body,Representation of belonging to a regionUnmanned aerial vehicle of (2) is in the firstAt the moment ofThe probability of not being infected is that,Indicating that the unmanned aerial vehicle is inProbability of not obtaining a patch; Representation unmanned aerial vehicle In the first placeAt the moment ofIs a function of the probability of (1),Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a function of the probability of (1),Indicating that the unmanned aerial vehicle is inBecause of the probability that the patch is installed to clear the virus,Representation of belonging to a regionUnmanned aerial vehicle of (2) is in the firstAt the moment ofThe probability of not being infected is that,Representation unmanned aerial vehicleIn the first placeAt the moment ofIs a probability of (2).
The equation (16) corresponds to the equation (6), the equation (17) corresponds to the equation (7), and the equation (18) corresponds to the equation (8).
In practical application, the normalization condition of the dynamic model is kept unchanged corresponding to each moment, and the normalization condition is specifically as follows:
（19）
the feasible region of the dynamic model is represented by the following formula:
（20）
wherein, ，，. By iterative solution, the time trace of the race dynamics at any given initial condition can be tracked.
Based on the same inventive concept, the embodiment of the invention provides a virus propagation dynamics modeling device, and because the principle of the device for solving the technical problem is similar to that of a virus propagation dynamics modeling method, the implementation of the device can be referred to the implementation of the method, and the repetition is omitted.
As shown in fig. 8, the apparatus includes a first determination unit 801, a second determination unit 802, a transmission unit 803, and an obtaining unit 804.
A first determining unit 801 for determining that the unmanned aerial vehicle is at the first positionThe probability of the state where the moment is located and the probability transition tree of the physical state are obtained from the unmanned aerial vehicle at the first placeProbability of the state at the moment; wherein the state comprises patch installation and easy infectionPatch is not installed and is easy to be infectedAnd installed and infected with patch; Before the launching, according to the unmanned plane beingIs in the unmanned planeDetermining that the unmanned aerial vehicle is in the probability of the supervisory layer, the adjacency matrix of the supervisory layer and the patch distribution rateProbability of not obtaining a patch;
A second determining unit 802, configured to, after transmission, fly at least one unmanned aerial vehicle from the first area to the second area, where the unmanned aerial vehicle located in the first area is located according to a probability of leaving to execute the task Probability of not being infected by the same area, unmanned aerial vehicle located in first area is inProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedProbability of not being infected by the same area, unmanned aerial vehicle located in second area is locatedThe probability of being not infected by the same area and the task layer normalized adjacency matrix sequentially determine that unmanned aerial vehicles belonging to the first area are in the first areaAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofProbability of not being infected;
A sending unit 803, configured to send a patch to an infected unmanned aerial vehicle if any one unmanned aerial vehicle is confirmed to be infected, so that the infected unmanned aerial vehicle performs virus removal based on the patch;
a obtaining unit 804, configured to, according to the presence of the unmanned aerial vehicle Probability of not obtaining patch, unmanned aerial vehicle is inDue to the probability of virus removal by installing patches, the unmanned aerial vehicle is inProbability of losing immunity, unmanned aerial vehicle belonging to first area is in the firstAt the moment ofProbability of not being infected and unmanned aerial vehicle belonging to first area in the firstAt the moment ofThe probability of not being infected is obtained and the unmanned plane is at the firstA dynamic model based on Markov chains corresponding to the probability of the state at the moment.
It should be understood that the above-mentioned virus propagation dynamics modeling apparatus includes units that are only logically divided according to functions implemented by the device, and in practical applications, superposition or splitting of the above units may be performed. The functions of the virus propagation dynamics modeling apparatus provided in this embodiment are in one-to-one correspondence with those of the virus propagation dynamics modeling method provided in the above embodiment, and the detailed process flow of the apparatus is described in detail in the above method embodiment one, and will not be described in detail here.
Another embodiment of the present invention also provides a computer apparatus, including: a processor and a memory; the memory is used for storing computer program codes, and the computer program codes comprise computer instructions; when the processor executes the computer instructions, the electronic device performs the steps of modeling virus propagation dynamics in the method flow shown in the method embodiment.
Another embodiment of the present invention also provides a computer readable storage medium, where computer instructions are stored, which when executed on a computer device, cause the computer device to perform the steps of modeling virus propagation dynamics in the method flow shown in the above method embodiment.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (10)
1. A method of modeling virus propagation kinetics, comprising:
Obtaining the probability of the state of the unmanned aerial vehicle at the t+1th moment according to the probability of the state of the unmanned aerial vehicle at the t moment and the probability transition tree of the physical state; wherein the states include patch installed and susceptible to PS, patch uninstalled and susceptible to US, and patch installed and susceptible to PI;
Before transmitting, determining the probability that the unmanned aerial vehicle is in US and does not acquire a patch according to the probability that the unmanned aerial vehicle is in PS, the probability that the unmanned aerial vehicle is in PI, the adjacency matrix of a supervision layer and the patch distribution rate;
After the unmanned aerial vehicle is transmitted, at least one unmanned aerial vehicle flies from a first area to a second area, and the probability that the unmanned aerial vehicle in the first area is not infected by the same area, the probability that the unmanned aerial vehicle in the second area is not infected by the same area and a task layer normalization adjacency matrix sequentially determine the probability that the unmanned aerial vehicle in the first area is not infected by the US at the t moment and the probability that the unmanned aerial vehicle in the first area is not infected by the PS at the t moment;
If any unmanned aerial vehicle is confirmed to be infected, a patch is sent to the infected unmanned aerial vehicle, so that the infected unmanned aerial vehicle can clear viruses based on the patch;
And obtaining a dynamic model based on Markov chains, which corresponds to the probability that the unmanned aerial vehicle is in a state at the t+1 time, according to the probability that the unmanned aerial vehicle is in the US and does not obtain a patch, the probability that the unmanned aerial vehicle is in the PI and removes viruses due to the installation of the patch, the probability that the unmanned aerial vehicle is in the PS and loses immunity, the probability that the unmanned aerial vehicle belonging to the first area is in the US and is not infected at the t time and the probability that the unmanned aerial vehicle belonging to the first area is in the PS and is not infected at the t time.
2. The method of modeling virus propagation kinetics of claim 1, wherein the markov chain based dynamic model is as follows:
wherein, Representing the probability that unmanned plane i is in US at time t+1,/>Representing probability of unmanned plane i being in PS at t-th moment,/>Represents the probability that unmanned plane i is in US at the t moment, delta represents the probability that unmanned plane is in PS and loses immunity, and is/isRepresenting the probability that the unmanned aerial vehicle belonging to the region k is in US and is not infected at the t-th moment, and r i (t) represents the probability that the unmanned aerial vehicle is in US and does not acquire a patch; /(I)Representing the probability that unmanned plane i is at PS at time t+1,/>Represents the probability that unmanned plane i is in PI at the t-th moment, mu represents the probability that unmanned plane i is in PI and viruses are removed due to the installation of patches,/>Representing the probability that unmanned aerial vehicle belonging to region k is in PS not infected at time t,/>The probability that the unmanned plane i is at PI at time t+1 is shown.
3. The method of modeling virus propagation kinetics of claim 1, wherein the probability that the unmanned aerial vehicle in the second region is in a state where US is not infected by the same region is expressed by the following formula:
The probability that the unmanned aerial vehicle located in the second area is in the PS and is not infected by the same area is expressed by the following formula:
wherein, Representing the probability that an unmanned aerial vehicle located in a second area is in a state that US is not infected by the same area,/>Representing the density of unmanned aerial vehicles in PI in region k,/> Represents the probability that unmanned plane i is in PI at the t-th moment, c ki represents the interlayer connecting edge of a task layer and a supervision layer, beta U represents the average probability that the unmanned plane is infected under the condition that US does not have a defense strategy, and/ > Representing the probability that a drone located in zone l is not infected after US randomly selects to communicate with a drone flying from zone k, n k→l represents the expected number of drones flying from zone k to zone l at time t,/>Representing the probability that the unmanned aerial vehicle located in the second area is not infected by the same area in PS, beta P represents the average probability that the unmanned aerial vehicle is infected under the condition that the PS has a defense strategy, M represents the area number of the task layer, and n k represents the unmanned aerial vehicle number included in the area k of the task layer G 2.
4. The method of modeling virus propagation kinetics according to claim 1, wherein the probability that the unmanned aerial vehicle belonging to the first region is not infected with US at time t is expressed by the following formula:
The probability that the unmanned aerial vehicle belonging to the first area is in PS and is not infected at the t moment is expressed by the following formula:
wherein, Representing the probability that an unmanned aerial vehicle belonging to a first area is not infected at US at time t, g representing the probability of leaving to perform a task,/>Representing the probability that an unmanned aerial vehicle located in a first area is in US and is not infected by the same area, R kl represents a task layer normalized adjacency matrix,/>Representing a probability that the drone located in the second area is in a region where US is not infected by the same region; /(I)Representing the probability that unmanned aerial vehicle belonging to the first area is at PS not infected at time t,/>Representing the probability that an unmanned aerial vehicle located in a first area is in a PS not infected by the same area,/>Indicating the probability that the drone located in the second zone is in a PS that is not infected by the same zone.
5. The method of modeling virus propagation dynamics according to claim 1, wherein the drone is at a probability that US does not obtain a patch from a neighbor drone, as follows:
wherein, Representing the probability of installing a patch at time t of unmanned plane i,/> Representing probability of being in PI at t-th moment of unmanned plane i,/>The probability that the unmanned aerial vehicle i is in PS at the t-th moment is represented, lambda represents the patch distribution rate, a ij represents the adjacency matrix of the supervision layer, r i (t) represents the probability that the unmanned aerial vehicle is in US and does not acquire patches from the neighbor unmanned aerial vehicles, and N represents the number of unmanned aerial vehicles.
6. The method for modeling virus propagation dynamics according to claim 1, wherein the probability of the state of the unmanned aerial vehicle at time t+1 is obtained based on a physical state probability transition tree as follows:
wherein, Representing the probability that unmanned plane i is in US at time t+1,/>Representing the probability that unmanned plane i is at PS at time t+1,/>Represents the probability that unmanned plane i is at PI at time t+1st,/>Representing probability of unmanned plane i being in PS at t-th moment,/>Represents the probability that unmanned plane i is in US at time t,Representing probability of being in PI at t-th moment of unmanned plane i,/>The probability that the unmanned plane i is converted from the state X to Y at the t-th moment is represented, X, Y epsilon { PI, PS, US }.
7. The method for modeling virus propagation dynamics according to claim 1, wherein before the probability of the state of the unmanned aerial vehicle at the time t+1 is obtained according to the probability of the state of the unmanned aerial vehicle at the time t and the probability transition tree of the physical state, the method further comprises:
Constructing a multi-layer network model consisting of a supervision layer and a task layer, wherein the supervision layer comprises a plurality of first nodes which are unmanned planes, and the connection edges among the first nodes represent communication connection in a satellite or cellular network;
the task layer comprises a plurality of second nodes which represent areas where the unmanned aerial vehicle can communicate with each other, and the connecting edges among the plurality of second nodes represent the flight route of the unmanned aerial vehicle.
8. A viral propagation dynamics modeling apparatus, comprising:
The first determining unit is used for obtaining the probability of the state of the unmanned aerial vehicle at the t+1th moment according to the probability of the state of the unmanned aerial vehicle at the t moment and the physical state probability transition tree; wherein the states include patch installed and susceptible to PS, patch uninstalled and susceptible to US, and patch installed and susceptible to PI; before transmitting, determining the probability that the unmanned aerial vehicle is in US and does not acquire a patch according to the probability that the unmanned aerial vehicle is in PS, the probability that the unmanned aerial vehicle is in PI, the adjacency matrix of a supervision layer and the patch distribution rate;
The second determining unit is used for sequentially determining the probability that the unmanned aerial vehicle belonging to the first area is not infected by US at the t moment and the probability that the unmanned aerial vehicle belonging to the first area is not infected by PS at the t moment according to the probability that the unmanned aerial vehicle leaving the first area is not infected by US at the same area, the probability that the unmanned aerial vehicle in the first area is not infected by PS at the same area, the probability that the unmanned aerial vehicle in the second area is not infected by PS at the same area and the task layer normalized adjacency matrix;
a sending unit, configured to send a patch to an infected unmanned aerial vehicle if any one unmanned aerial vehicle is confirmed to be infected, so that the infected unmanned aerial vehicle performs virus removal based on the patch;
The obtaining unit is used for obtaining a dynamic model based on Markov chains, which corresponds to the probability that the unmanned aerial vehicle is in the state of the unmanned aerial vehicle at the t+1st moment according to the probability that the unmanned aerial vehicle is in the US and does not obtain the patch, the probability that the unmanned aerial vehicle is in the PI and removes viruses due to the installation of the patch, the probability that the unmanned aerial vehicle is in the PS and loses immunity, the probability that the unmanned aerial vehicle belonging to the first area is in the US and is not infected at the t moment and the probability that the unmanned aerial vehicle belonging to the first area is in the PS and is not infected at the t moment.
9. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the virus propagation dynamics modeling method according to any one of claims 1-7.
10. A computer readable storage medium, characterized in that a computer program is stored, which computer program, when being executed by a processor, causes the processor to perform the method of modeling virus propagation dynamics according to any one of claims 1-7.
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