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Understanding the Spreading Patterns of Mobile Phone Viruses


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Sasahara Lab's Journal club 2014/6/3

Published in: Science
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Understanding the Spreading Patterns of Mobile Phone Viruses

  1. 1. Understanding the Spreading Patterns of Mobile Phone Viruses P. Wang, M. C. González, C. A. Hidalgo, and A.-L. Barabási Science, 2009 JClub 2014.06.03 by K. Sasahara
  2. 2. Introduction n  Background n  Traditional cellphones are relatively immune to viruses for the lack of standardized operating system. n  Smart phones have the possibility of mobile virus outbreaks. n  Objectives To study the spreading patterns of mobile viruses, we model the mobility of mobile phone users.
  3. 3. Spread of Mobile Viruses n  Two dominant protocols: BT and MMS Address book Long-range Local
  4. 4. Tracking Mobility Patterns of Mobile Phone Users n  Mobile phone users data n  Anonymized billing record of mobile phone provider n  Calling patterns n  Coordinates of the closest mobile phone tower n  Simulation n  A BT viruse can infect mobile phones within r=10m. n  Once infected with an MMS virus, the phone sends a copy to all phones in the address book within 2min. n  SI model
  5. 5. SI Model n  Susceptible users (S) are infected by infected users (I). n  # of infected users evolves in time as follows: dI dt = β SI N β = µ < k > : the effective infection rate (here µ =1) N: Number of users in the tower area < k > =ρA: the average number of contacts ρ = N Atower : population density A = πr2 : BT communication area
  6. 6. Temporal Patterns in the Spread of BT and MMS Viruses n  The spreading rate (I/N) depends on the handset s market share (m) in both viruses. n  BT viruses can reach all susceptible handsets but slowly (days) for human mobility. n  MMS viruses can reach only a few fraction of handsets but quickly (hours) for the fragmentation of the call network.
  7. 7. Market Share-driven Phase Transition n  The fragmentation of the call network is governed by a percolation phrase transition at mc=0.095 in MMS viruses. ↑   m2009 < 0.03 ▽: Saturation value in Fig. 2B
  8. 8. Subset of the Real Call Network n  The size of the giant component depends on the handset s market share (m1 =0.75, m2 =0.25). Giant connected component
  9. 9. Latency Time n  The latency time (T) is highly sensitive to market share (m). n  T divergence occurs at m=0 in BT case and at a finite m (>0) n  Gm act as a critical point: T(q > Gm, m) = n  There are factors beyond Lmax that contribute to T  divergence in MMS case ((m-m*)-α(q)).
  10. 10. Spatial Patterns in the Spread of Viruses Wave-like patterns Delocalized patterns <D> depends on protocol not on m
  11. 11. Temporal Patterns in the Spread of Hybrid Viruses n  Hybrid virus (e.g., CommWarrior) n  For high m, Hybrid virus dominates spreading pattern. n  For low m, Hybrid virus behaves like BT virus in T n  Hybrid virus is 3x faster than MMS virus for m > mc.
  12. 12. Summary n  The spread of a BT virus is rather slow because of human mobility. n  An MMS virus can reach only a small fraction of users because of the fragmentation of the call network. n  Hybrid viruses shows a complex market share dependence, resulting from a nontrivial superposition of the BT and MMS spreading modes. n  The outbreak of mobile viruses has not happened so far; however, once a market share reaches the phase transition point, it will happen.