Patent Publication Number: US-2023161874-A1

Title: Malware protection based on final infection size

Description:
PRIORITY CLAIM 
     The present application is a National Phase entry of PCT Application No. PCT/EP2021/058360, filed Mar. 30, 2021, which claims priority from EP Patent Application No. 20168112.9, filed Apr. 3, 2020 each of which is hereby fully incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to the automatic forecasting of malware propagation across a set of computer systems. 
     BACKGROUND 
     Conventional malware protection mechanisms are reactive to the detection of malware in a network or the widespread distribution of anti-malware measures. Such approaches are known as “diagnosis and treatment”. Similar techniques are used to combat the spread of biological infections. Mitigation measures such as anti-malware or malware-specific protective measures may not be known for some time after an infection has been studied for its effects. 
     SUMMARY 
     Accordingly, it is beneficial to provide improvements to the deployment of protections for malware for sets of computer systems. 
     According to a first aspect of the present disclosure, there is provided a computer implemented malware protection method to protect at least a subset of computer systems in a population of network-connected computer systems, the method comprising: identifying a plurality of clusters of computer systems in the population wherein computer systems within each cluster share at least one common characteristic; determining a distribution of predicted final infection size for the population as a total number of systems infected by a propagation of a malware in the population, the distribution including predictions for infections originating with systems in the population, each predicted final infection size being determined by a forecasting simulation of malware propagation from an originating system in the population, the simulation being performed based on at least one malware propagation model defining at least a transmission rate of malware between systems in the population determined to be in communication with each other, and a removal rate of systems being removed from a state of infection by the malware; determining a plurality of ranges of final infection size from the distribution; determining weighted associations between clusters of computer systems and ranges of final infection size based on measures of numbers of originating computer systems in each cluster associated with each range of final infection size; deploying protective measures for one or more clusters of computer systems responsive to the weighted associations. 
     In some embodiments, the at least one common characteristic includes: a logical or physical position of computer systems in the population; a network attribute of computer systems in the population; a predetermined role or function of computer systems in the population; and a common type of device of computer systems in the population. 
     In some embodiments, the at least one malware propagation model identifies interacting pairs of the computer systems in the population based on interactions corresponding to previous communication occurring between the computer systems in the pair. 
     In some embodiments, the forecasting simulation includes simulating, over a plurality of simulated time periods, a propagation of the malware from an originating system in the population, the simulation being based on a number of interactions per time period between each interacting pair of computer systems in the population, the transmission rate and the removal rate. 
     In some embodiments, the distribution includes predictions for infections originating with each system in the population. 
     In some embodiments, the plurality of ranges of final infection size is determined by: determining a probability of each final infection size in the distribution to generate a signal indicating a range of probabilities for each final infection size, the signal being processed to reduce noise therein; determining the plurality of ranges of final infection size based on the signal. 
     In some embodiments, the plurality of ranges of final infection size are determined based on the signal by dividing the signal into the plurality of ranges based on the identification of local minima in the signal. 
     In some embodiments, the protective measures include one or more of: an anti-malware facility; a malware filter; a malware detector; a block, preclusion or cessation of interaction; and a reconfiguration of one or more computer systems. 
     According to a second aspect of the present disclosure, there is a provided a computer system including a processor and memory storing computer program code for performing the method set out above. 
     According to a third aspect of the present disclosure, there is a provided a computer system including a processor and memory storing computer program code for performing the method set out above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present disclosure will now be described, by way of example only, with reference to the accompanying drawings, in which: 
         FIG.  1    is a block diagram a computer system suitable for the operation of embodiments of the present disclosure. 
         FIG.  2    is a component diagram of an arrangement for malware protection for at least a subset of a set of computer systems. 
         FIG.  3    is a flowchart of a malware protection method. 
         FIG.  4    is a component diagram of an arrangement for malware protection for at least a subset of a set of computer systems. 
         FIG.  5    is a flowchart of a malware protection method. 
         FIG.  6    is a component diagram of an arrangement of an arrangement for malware protection for at least a subset of a set of computers in accordance with embodiments of the present disclosure. 
         FIG.  7    is a flowchart of a malware protection method in accordance with embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIG.  1    is a block diagram of a computer system suitable for the operation of embodiments of the present disclosure. A central processor unit (CPU)  102  is communicatively connected to a storage  104  and an input/output (I/O) interface  106  via a data bus  108 . The storage  104  can be any read/write storage device such as a random-access memory (RAM) or a non-volatile storage device. An example of a non-volatile storage device includes a disk or tape storage device. The I/O interface  106  is an interface to devices for the input or output of data, or for both input and output of data. Examples of I/O devices connectable to I/O interface  106  include a keyboard, a mouse, a display (such as a monitor) and a network connection. 
     Malicious software, also known as computer contaminants or malware, is software that is intended to do direct or indirect harm in relation to one or more computer systems. Such harm can manifest as the disruption or prevention of the operation of all or part of a computer system, accessing private, sensitive, secure and/or secret data, software and/or resources of computing facilities, or the performance of illicit, illegal or fraudulent acts. Malware includes, inter alia, computer viruses, worms, botnets, trojans, spyware, adware, rootkits, keyloggers, dialers, malicious browser extensions or plugins and rogue security software. 
     Malware proliferation can occur in a number of ways. Malware can be communicated as part of an email such as an attachment or embedding. Alternatively, malware can be disguised as, or embedded, appended or otherwise communicated with or within, genuine software. Some malware is able to propagate via storage devices such as removable, mobile or portable storage including memory cards, disk drives, memory sticks and the like, or via shared or network attached storage. Malware can also be communicated over computer network connections such as the internet via websites or other network facilities or resources. Malware can propagate by exploiting vulnerabilities in computer systems such as vulnerabilities in software or hardware components including software applications, browsers, operating systems, device drivers or networking, interface or storage hardware. 
     A vulnerability is a weakness in a computer system, such as a computer, operating system, network of connected computers or one or more software components such as applications. Such weaknesses can manifest as defects, errors or bugs in software code that present an exploitable security weakness. An example of such a weakness is a buffer-overrun vulnerability, in which, in one form, an interface designed to store data in an area of memory allows a caller to supply more data than will fit in the area of memory. The extra data can overwrite executable code stored in the memory and thus such a weakness can permit the storage of malicious executable code within an executable area of memory. An example of such malicious executable code is known as ‘shellcode’ which can be used to exploit a vulnerability by, for example, the execution, installation and/or reconfiguration of resources in a computer system. Such weaknesses, once exploited, can bootstrap a process of greater exploitation of a target system, and propagation of the malware to other computer systems. 
     The effects of malware on the operation and/or security of a computer system lead to a need to identify malware in a computer system in order to implement protective and/or remedial measures. While malware detection is often directed to computer systems themselves or the networks over which they communicate, interactions between computer systems can transcend the physical interconnections therebetween. In particular, interactions between computer systems that arise from communication between pairs of computer systems can be addressed. Such interactions can include, for example, interactions between users of each of a pair of computer systems using, inter alia, social media, messaging, electronic mail or file sharing facilities. Thus, a model of a set of computer systems in which interacting pairs of computer systems are identified can be employed, such interactions being based on previous communication occurring between the computer systems in the pair. Notably, such a model disregards intermediates in an interaction—such as physical resources or other computer systems involved in a communication. For example, an interaction arising from a social media communication between two users using each of a pair of computer systems will involve potentially multiple physical or logical networks, intermediate servers, service provider hosts, intermediate communication appliances and the like. Thus, a model of the physical communication becomes burdened by the intermediate features of a typical inter-computer communication. In contrast, the endpoints of an interaction such as the computer systems through which users communicate can be addressed. A similar analysis can be conducted for interactions involving email, electronic messaging, file sharing and the like. 
     The deployment of malware protection measures to inhibit a propagation of a malware through a set of computer systems is desirable. Most preferably, the deployment of malware protection measures is targeted to provide an effective and/or efficient inhibition of the propagation. The nature and type of malware protection measures themselves are understood by those skilled in the art and can include, inter alia: anti-malware facilities; malware filters; malware detectors; a block, preclusion or cessation of interaction and/or communication, such as between computer systems; and/or a reconfiguration of one or more computer systems or communications facilities therebetween. 
     Computer systems or interacting pairs of computer systems can be identified for the deployment of malware protection measures based on a simulation of a propagation of malware through the model of a set of computer systems. Such simulation can employ simulation parameters including: a rate of interaction between each interacting pair of computer systems (i.e. a number of interactions per time period); and a rate of transmission of the malware between interacting computer per interaction. Some or all of these parameters can be derived statistically according to a statistical distribution. Some or all of these parameters can be determined based on historical interaction information over a historical time period. Some or all of these parameters can be determined based on one or more machine learning processes based on historical interaction information. 
       FIG.  2    is a component diagram of an arrangement for malware protection for at least a subset of a set of computer systems. A model  200  is provided as one or more data structures representing a set of computer systems and interactions therebetween. In some embodiments, the model is provided as a graph or similar data structure including nodes or vertices  210 , each corresponding to a computer system, and edges  212  each connecting a pair of nodes  210  and representing interaction between computer systems corresponding to each node in the pair. Thus, an edge  212  represents interaction between a pair of computer systems. Each node  210  can have associated information for a corresponding computer system including, for example, inter alia: an identifier of the computer system; an identification of an organizational affiliation of the computer system; an identifier of a subnet to which the computer system is connected; and other information as will be apparent to those skilled in the art. 
     In some embodiments, an edge  212  constitutes an indication that at least one interaction has taken place over at least a predetermined historic time period between computer systems in a pair. In some embodiments, the existence of an edge  212  is not determinative, indicative or reflective of a degree, frequency or propensity of interaction between computer systems in a pair—rather, the edge  212  identifies that interaction has taken place. Edges  212  can have associated, for example, inter alia: an edge identifier; an identification of a pair of nodes (and/or the corresponding computer systems) that the edge interconnects; and/or interaction frequency information between a pair of computer systems. It will be appreciated by those skilled in the art that, while the model  200  is illustrated as a literal graph in the arrangement of  FIG.  2   , alternative data structures and logical representations of vertices and edges can be used, such as representations employing, for example, inter alia, vectors, arrays of vectors, matrices, compressed data structures and the like. 
     The arrangement of  FIG.  2    includes a simulator  202  as a hardware, software, firmware or combination component arranged to perform a simulation of a propagation of a malware in the set of computer systems represented by the model  200 . The simulator  202  is operable on the basis of simulation parameters including: an interaction rate  204  as a number of interactions between pairs of interacting computer systems in a time period; and a transmission rate  206  as a rate of transmission of a malware between computer systems in a pair of systems per interaction. In some embodiments, the transmission rate  206  is a probability of transmission of a malware from one node to another node during an interaction between the nodes. In some embodiments, the transmission rate  206  incorporates aspects of a malware infection process. For example, in the case of malware transmitted as a web-link between two computer systems by email, the transmission rate can reflect all of: a probability that an email is communicated between the two computer systems; a probability that the email includes the malicious web-link; and a probability that a recipient accesses the malicious web-link resulting in malware infection. 
     The interactions rate  204  can be sampled from one or more statistical distributions  214  to model different types of interaction. For example, a Poisson or uniform distribution can be used to model a number of interactions between a pair of computer systems over a time period, such as a number of emails communicated over the time period. The transmission rate  206  can be initialized in advance, such as by a predetermined value. For example, a transmission rate  206  having a value of 0.0001 is indicative of a probability that a first computer system in an interacting pair of computer systems transmits a malware to a second computer system in the pair within a single predetermined time period is 0.0001. The interaction rate  204  between each of an interacting pair of computer systems in the set of computer systems can be defined based on historical records of interactions between the computer systems. 
     The simulator  202  can operate on the basis of configurable characteristics such as simulation assumptions. For example, the simulator  202  may operate on the basis that any computer system as represented by a node in the model  200  can only transmit the malware to first-degree neighbors according to the model  200 . Further, the simulator  202  preferably operates on the basis that each computer system has a state of infection at a point in time. States of infection at a point in time can include, for example: a state of susceptibility in which a computer system is susceptible to infection, such as a computer system that is not and has not been so far infected and is not specifically protected from infection by a particular malware; a state of infected in which a computer system is subject to infection by the malware at the point in time; and a state of removed or remediated in which a computer system is remediated of a past infection or protected from prospective infection by the malware. It will be appreciated by those skilled in the art that sub-states of these states can also be employed, such as, inter alia: an infected state that is not infectious (i.e. transmission of malware cannot be effected by a computer system in such a state); an infected state that is infectious; an infected state that is detected; and an infected state that is not detected (such as might be determined by the simulator  202 ). 
     Thus, in use, the simulator  202  is operable for a time period to model the propagation of a malware infection. One or more predetermined source computer systems represented in the model  200  can be selected as originating computer systems for the malware infection such that propagation is simulated from such originating computer systems. In some embodiments, the simulator  202  is executed for each of a plurality of time periods so as to model the propagation of the malware in the set of computer systems over time. Additionally or alternatively, the simulator  202  can be performed a plurality of times for each of a plurality of predetermined source computer systems selected as originating computer systems for the malware infection. 
     For example, if the transmission rate  206  is denoted as p, and the interaction rate  204  is denoted as c, the simulator  202  can model propagation of a malware by formulating an infection probability of a susceptible computer system indicated as node i by its infected neighbors: 
       Considering node i  where  i ∈{1 , . . . ,n } where  n =number of nodes in the model,
 
       node i &#39;s infectious neighbours  Nhb   i,j   ={nhb   i,1   , . . . ,nhb   i,m     (i)   }         where j∈{1, . . . , m (i) } and m i  ∈  is the number of neighbours of node i          
     The corresponding set of interactions are Inter i,j ={c i,1 , . . . ,c i,m (i)}. 
     
       
         
           
             
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     Thus, an exemplary model for the simulator  202  to model transitions of nodes  210  from a state of susceptible to infected and from infected to removed (i.e. remediated) can be: 
                                                Probability of a node transitioning from a   1 − (1 −              susceptible state to an infected state           Probability of a node in a susceptible state   (1 −              remaining in the susceptible state           Probability of a node transitioning from an   θ r             infected state to a removed state           Probability of a node in an infected state   1 − θ r             remaining in the infected state           Probability of a node in the removed state   1           remaining in the removed state                        
where θ is a rate of removal/remediation.
 
     Responsive to the simulation by the simulator  202 , and, in particular, responsive to the model of propagation of a malware determined by the simulator  202 , a protector component  208  is operable to deploy malware protection measures intended to inhibit a propagation of the malware through the set of computer systems. The protector component  208  is a hardware, software, firmware or combination component arranged to access output from the simulator  202  such as one or more models, data structure representations, images, animations, visually renderable indications or other suitable representations of states of nodes corresponding to simulated states of computer systems in the set of computer systems. For example, a representation of states of computer systems can be provided based on the model  200  so as to indicate, for each computer system by way of a node in the model  200 , a state of the computer system (such as susceptible, infected, removed) over each of a plurality of time periods for which the simulator  202  was executed. 
     The protector  208  identifies one or more computer systems or interacting pairs of computer systems (such as are represented by edges  212  in the model  200 ) for the deployment of malware protection measures. Such identified systems or pairs of systems can be selected based on, for example, inter alia: a computer system or interacting pair of systems through which malware propagates in the simulation to a subset of other computer systems in the set of computer systems; identifying a subset of computer systems having a relatively greater, or greatest, proportion of computer systems infected by the malware according to the simulation, so as to identify one or more computer systems or pairs of systems as a gateway, link or bridge to such identified subset; a number of computer systems to which the malware is propagated via a computer system or pair of systems; and other criteria as will be apparent to those skilled in the art. For example, “choke-points” in the model  200  can be identified by the protector  208  based on the simulator  202  output as nodes or pairs of nodes representing computer systems or interacting pairs of systems constituting pathways for propagation of the malware to subsets of nodes in the model  200 . The malware protection measures deployed by the protector  208  can include those previously described, and in this way at least a subset of the set of computer systems can be protected from the malware by the targeted deployment of malware protection measures. 
     The model  200  can further identify a class of interaction between interacting pairs of computer systems, such as an identification of a type of interaction that takes place between computer systems. For example, computer systems that typically interact by way of email can be classified differently to computer systems that typically interact by way of file-sharing, network drive sharing or the like. A class of interaction between computer systems can be determined based on historical records of interactions between each computer system in an interacting pair. Thus, the rate of transmission  206  of the malware per interaction can be determined for each interacting pair of computer systems based on the class of interaction for the interacting pair so as to take account of the different types of interaction and a different propensity for malware propagation by each type. 
       FIG.  3    is a flowchart of a malware protection method. Initially, at  302 , the method accesses a model of a set of computer systems identifying interacting pairs of the computer systems based on interactions corresponding to previous communication occurring between the computer systems in the pair. At  304  the method commences an iteration between each of a plurality of time periods for simulation. At  306 , for each simulated time period, the method simulates a propagation of a malware originating from a predetermined source computer system in the model. The simulation is based on a number of interactions per time period  204  between each interacting pair of computer systems in the set, and a rate of transmission  206  of the malware per interaction. The method loops at  308  through the time periods. Subsequently, at  310  the method identifies one or more computer systems or interacting pairs of computer systems for the deployment of a malware protection measure to inhibit a propagation of the malware through the set of computer systems. 
       FIG.  4    is a component diagram of an arrangement for malware protection for at least a subset of a set of computer systems. Many of the elements of  FIG.  4    are identical to those described above with respect to  FIG.  2    and these will not be repeated here. The arrangement of  FIG.  4    is operable during an infection, by a malware, of one or more computer systems in the set of computer systems and, accordingly, nodes  210  in the model  200  include indications of an infection state as, at least, susceptible or infected. Thus, the arrangement of  FIG.  4    is operable during an infection such as in real-time while an infection is occurring in the set of computer systems. 
     According to the arrangement of  FIG.  4   , the transmission rate  404  is determined based on a set of temporal historical interaction data  406 . The temporal historical interaction data  406  identifies interactions  408  between pairs of computer systems represented in the model  200  during each of a plurality of historical time periods—the time period being historical in that they occur prior to the operation of the simulator  202 . A transmission rate estimator  402  is provided as a hardware, software, firmware or combination component for estimating a transmission rate  404  for input to the simulator  202  based on the temporal historical interaction data  406 . The transmission rate estimator  402  can be operable to determine the rate of transmission  404  by modeling probabilities of transmission of the malware between interacting pairs of computer systems identified in the temporal historical interaction data. 
     In some embodiments, the transmission rate estimator  402  determines a maximum likelihood function for interactions occurring in each of a plurality of time periods for the historical interaction data  406  to determine an average probability of transmission of the malware between interacting pairs of computer systems. Additionally or alternatively, the probabilities of transmission can be modelled using a suitable statistical modeling function such as a Markov Chain Monte Carlo method for approximation of a probability as will be understood by those skilled in the art. 
     Accordingly, arrangements according to  FIG.  4    employ interaction data  408  indicating actual frequencies of interactions between computer systems represented in the model  200 . Such interaction data can be directed such that, for a computer system (node in the model  200 ), only incoming edges (along which interactions are received) are considered prospective transmitters of malware. The interaction data  408  is temporal in that it is broken down into time periods in order that historic malware infection propagation can be modelled on a suitable time-based granularity (such as by minute, hour, day). A number of interactions with a susceptible target (i.e. endpoint of an interaction) computer system from only infected source (i.e. originating) computer system can be identified in the interaction data  408 . By way of rationalizing interaction data  408 , interactions between interacting pairs of computer systems can be represented as a summary or summation of total incoming interactions from infected neighbors per time period for input to the transmission rate estimator  402 . 
     The transmission rate estimator  402  can determines a maximum likelihood function to estimate the transmission rate  404  according to a method such as: 
     Input: time: T 
     list of vector of interactions: c 
     number of nodes: n 
     list of binary vectors length n,
         containing 1 for infected,   containing 0 for susceptible nodes:y
 
Output: average infection transmission rate per interaction: p
 
For each time period in T:
       

     create vector of results 
     For each susceptible node:
         sum all interactions c from infected nodes   input summed interactions, binary vector y to
           maximum likelihood function   
           apply log transformation to the maximum likelihood function   minimize the log transformed function   append result of minimization to vector of results       

     return mean of vector of results 
       FIG.  5    is a flowchart of a malware protection method. Many of the operations of  FIG.  5    are identical to those described above with respect to  FIG.  3    and these will not be repeated here. Additionally,  FIG.  5    includes operation  503 , according to which a rate of transmission of malware per interaction is estimated by the transmission rate estimator as described above. 
     Embodiments of the present disclosure employ an approach to deploying malware protective measures based on a metric of final infection size in a population of network-connected computer systems. A final infection size is a total number of systems in a population of systems that are infected by propagation of a malware in the population. In particular, embodiments of the present disclosure employ final infection size information that is predicted for a population of computer systems using a malware propagation model and simulation process such as those described in detail above with respect to  FIGS.  2  to  5   . A malware propagation model can include a model (such as model  200 ) of a population of systems, and parameters such as the interaction rate  204 , transmission rate  206  and a recovery, remediation or removal rate. Simulations according to the aforementioned exemplary processes or alternative suitable simulation processes are employed to generate a distribution of predicted final infection size. In some embodiments, simulations are performed for a malware infection originating at each system in the population. 
     Classes of final infection size are defined based on ranges within the distribution so as to determine a weighted associate of each range of final infection sizes with systems in the population. The ranges are preferably determined based on a determination of a probability of each final infection size. The probabilities so determined can be modelled such as by correlating a probability with each final infection size so as to generate a signal of probabilities. Such a signal can constitute a promising basis for dividing the distribution into ranges by, for example, local minima detection in the signal of probabilities where a local minima can constitute a point of separation between two ranges of final infection size. 
     The population of systems is divided into clusters of systems based on characteristics of the systems such as physical or logical position, network configuration, system type or the like. An association can thus be made between ranges of final infection sizes and each cluster of systems, the association being weighted according to a number of incidences, during simulation, that a malware infection beginning at systems in a cluster of systems resulted in a final infection size within a particular range of sizes. This association is used to determine clusters of systems for which additional malware controls or monitoring are occasioned. For example, the determination can be based on: a magnitude of a final infection size or a range of final infection sizes; a probability of a final infection size or range, median or mean of a range of final infection sizes; and a weight of an association between a cluster of systems and a range of final infection sizes. In this way, in dependence on, for example, a detection of an outbreak of a malware originating at a particular computer system or within a particular cluster of computer systems, appropriate and proportionate control responses can be deployed in view of the likelihood of a range of final infection sizes. 
       FIG.  6    is a component diagram of an arrangement of an arrangement for malware protection for at least a subset of a set of computers in accordance with embodiments of the present disclosure. A population  200  of network-connected computer systems is provided in which communications takes place between certain pairs of the computer systems, such communication constituting a potential conduit for the transmission of malware between the computer systems. A cluster component  610  is a hardware, software, firmware or combination component arranged to cluster the population of computer systems  600  into a clustered population  602  comprising a plurality of clusters  652 ,  654 ,  656 ,  658 ,  660 ,  662 ,  664 . Systems are clustered according to at least one common characteristic such as, inter alia: a logical or physical position of computer systems in the population; a network attribute of computer systems in the population; a predetermined role or function of computer systems in the population; and a common type of device of computer systems in the population. Such clustering can be undertaken by the cluster component  610  based on predetermined clustering rules based on the one or more characteristics, and/or using clustering algorithms based on such characteristics as are well known in the art. 
     A distribution generator  612  is provided as a hardware, software, firmware or combination component for determining a distribution  618  of predicted final infection size for the population  600 . The final infection size is a total number of systems infected in the population  600  by a propagation of a malware in the population  600 . Notably, a malware will propagate through systems in stages of vulnerable, infected and remediated/removed. The distribution  618  generated by the generator  612  includes one or more estimated final infection sizes for malware infections originating at each of a plurality of systems in the population  600  such that a distribution of all predicted final infection sizes across all such originating systems is generated. In some embodiments, final infection sizes are predicted for originating systems at least including systems in each cluster in the clustered population  602 . In one example embodiment, final infection sizes are predicted for malware originating at every system, and further most preferably multiple final infection sizes are predicted for each originating system. 
     The distribution generator  612  predicts the final infection size for an originating computer system by a simulation of malware propagation through the population  600  from the originating system using a simulator  616  such as has been previously described. The simulator  616  operates on the basis of at least one malware propagation model  614  including a definition of at least: a transmission rate of malware between systems in the population determined to be in communication with each other; and a removal rate of systems being removed from a state of infection by the malware. 
     In some embodiments the malware propagation model identifies interacting pairs of the computer systems in the population  600  based on interactions corresponding to previous communication occurring between the computer systems in the pair, such as has been described previously. Further, and in some embodiments, the simulator  616  simulates a propagation of the malware from an originating system in the population  600  over a plurality of simulated time periods where the simulation is based on a number of interactions per time period between each interacting pair of computer systems in the population, the transmission rate and the removal rate. 
     The distribution of predicted final infection size  618  is subsequently processed by an infection size range determiner  620  as a hardware, software, firmware or combination component arranged to determine multiple ranges  622  or classes of final infection size from the distribution  618 . Each range of infection size can be a continuous range of final infection sizes and, in some embodiments, is determined according to the following procedure. 
     Initially, a probability of each final infection size in the distribution is determined. This can be determined by comparing a frequency of occurrence of each final infection size in the distribution with the total number of final infection sizes in the distribution. The probabilities of all final infection sizes can be used to form a signal indicating a range of probabilities for each final infection size. In one example embodiment, the signal is processed to smooth and/or reduce noise therein, such as by the application of one or more suitable signal processing methods including Gaussian Kernel filter or Savitzky-Golay filter. The signal provides a useful basis for dividing the final infection sizes into classes or ranges  622 . For example, the ranges  622  of final infection size can be determined based on the signal by dividing the signal into the plurality of ranges  622  based on the identification of local minima in the signal (such minima indicating points of locally relatively lower probability of final infection size). In one embodiment, the number of ranges is constrained to a predetermined limit and, where a number of identified ranges exceeds this limit, adjacent ranges can be combined. 
     An associator  624  component is a hardware, software, firmware or combination component arranged to determine a weighted association between each cluster in the clustered population  602  and each range in the set of ranges of final infection size  622 . The associations by the associator  624  can be determined automatically based on the distribution  618  associating each originating system in the population  600  with a frequency of one or more final infection sizes arising from the malware propagation simulations, and the cluster membership information in the clustered population  602 . The weight of each association between a cluster and a range of final infection sizes can be determined, for example, based on a frequency of occurrence of each final infection size within the range arising from simulations for originating systems in the cluster. Thus, for example, a proportion of a cluster of systems contributing to final infection sizes within a range of sizes can be used to weight the association between the cluster and the range. 
     A deployer  626  component is provided as a hardware, software, firmware or combination component for deploying protective measures for one or more of the clusters of systems in the clustered population  602  in dependence on the weighted associations between clusters and ranges of final infection size. For example, the deployer  626  determines clusters of systems for additional malware controls or monitoring based on: a magnitude of a final infection size or a range of final infection sizes; a probability of a final infection size or range, median or mean of a range of final infection sizes; and a weight of an association between a cluster of systems and a range of final infection sizes. In this way, in dependence on, for example, a detection of an outbreak of a malware originating at a particular computer system or within a particular cluster of computer systems, appropriate and proportionate control responses can be deployed in view of the likelihood of a range of final infection sizes. Examples of protective measures that may be deployed by the deployer  626  include: an anti-malware facility; a malware filter; a malware detector; a block, preclusion or cessation of interaction; and a reconfiguration of one or more computer systems. 
       FIG.  7    is a flowchart of a malware protection method in accordance with embodiments of the present disclosure. Initially, at  702 , the method identifies clusters of computer systems in the population  600  based on the systems sharing at least one common characteristic. At  704  the method determines a distribution  618  of predicted final infection size for the population  600  including predictions for infections originating with systems in the population  600 . Each predicted final infection size is determined by a forecasting simulation of malware propagation from an originating system in the population. At  706  the method determines multiple ranges of final infection size from the distribution. At  708  the method determines weighted associations between clusters of computer systems and ranges of final infection size based on measures of numbers of originating computer systems in each cluster associated with each range of final infection. Subsequently, at  710 , the method deploys protective measures for one or more clusters of computer systems responsive to the weighted associations. 
     Insofar as embodiments of the disclosure described are implementable, at least in part, using a software-controlled programmable processing device, such as a microprocessor, digital signal processor or other processing device, data processing apparatus or system, it will be appreciated that a computer program for configuring a programmable device, apparatus or system to implement the foregoing described methods is envisaged as an aspect of the present disclosure. The computer program may be embodied as source code or undergo compilation for implementation on a processing device, apparatus or system or may be embodied as object code, for example. 
     Suitably, the computer program is stored on a carrier medium in machine or device readable form, for example in solid-state memory, magnetic memory such as disk or tape, optically or magneto-optically readable memory such as compact disk or digital versatile disk etc., and the processing device utilizes the program or a part thereof to configure it for operation. The computer program may be supplied from a remote source embodied in a communications medium such as an electronic signal, radio frequency carrier wave or optical carrier wave. Such carrier media are also envisaged as aspects of the present disclosure. 
     It will be understood by those skilled in the art that, although the present disclosure has been described in relation to the above described example embodiments, the disclosure is not limited thereto and that there are many possible variations and modifications which fall within the scope of the disclosure. 
     The scope of the present disclosure includes any novel features or combination of features disclosed herein. The applicant hereby gives notice that new claims may be formulated to such features or combination of features during prosecution of this application or of any such further applications derived therefrom. In particular, with reference to the appended claims, features from dependent claims may be combined with those of the independent claims and features from respective independent claims may be combined in any appropriate manner and not merely in the specific combinations enumerated in the claims.