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Virus Spread, Epidemic Threshold, Heterogeneous Networks, Diversification

The purpose of this article is to extend related research on the spread of malware in networks and to assess the security impact of certain measures against the spread of malware. We examine the influence of heterogeneous infection and curing rates for a Susceptible-Infected-Susceptible (SIS) model, that is used to describe the spread of malware on the Internet. The topology structure considered is the regular graph, which represents homogeneous network structures. We present a new method to calculate the steady state of heterogeneous populations, for the general case with m subpopulations. Using this method, we give the explicit conditions under which the malware persists in the network. Next we give calculation examples which are based on the assumption of two subpopulations and explore this method in more detail, proving that the method produces valid outcomes and that the basic reproduction numbers R for each subpopulation are the only factors determining the steady state situation. The value of R depends on the effectiveness of attacking malware and the defending countermeasures. We then consider some special cases for subpopulations in regular graphs using this method. In the first case the protection against malware is assumed to be absent within one subpopulation. The calculations show that it pays off for the subpopulations with the best protection to help other, less protected subpopulations. The second case describes the effect of diversification against malware, when one subpopulation does not share the vulnerabilities with the rest of the population to become infected with malware and propagate that malware. The results show that diversification is an effective countermeasure against the propagation of malware. Based on the market share of the software, we estimate the 'resistance' of different compartments against malware. Using statistical data, we finally show that dividing a population in two subpopulations increases the accuracy of the model. Based on this data, we also show that the use of security software does not correlate very well with the number of reported infections.