Sasahara Lab's Journal club 2014/6/3

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. 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. Spread of Mobile Viruses
n Two dominant protocols: BT and MMS
Address
book
Long-range
Local

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. 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. 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. 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. 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. 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. Spatial Patterns
in the Spread of Viruses
Wave-like
patterns
Delocalized
patterns
<D> depends on protocol
not on m

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. 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.