Introducing Epidemic Models for
Data Survivability in UWSNs
Roberto Di Pietro,
Nino Vincenzo Verde
{dipietro,nverde}@mat.uniroma3.it
Universita’ di Roma Tre
RoadMap
• UWSNs
• Epidemic Models
– SIR
– SIS
• Epidemic Models for Information Survivability in
UWSNs
– Modeling the problem
– Applications
– Results
• Conclusions
Unattended WSNs
• Sporadic presence of the sink
• Sensors upload info as soon as the sink comes
around
• Applications:
– Hostile environment
monitoring
– Pipeline monitoring
Information Survivability
• Sink not always available:
– More subject to malicious attacks than traditional
WSN
• Our target:
To provide a certain level of assurance about
Information Survivability
Epidemic Models
• Stochastic approaches
– Accurately describe fluctuation
– Variation chance in exposure risk
– Very complex
– Laborious to set up
Epidemic Models
• Deterministic approaches
– Describe the dynamic of a disease at the population
scale
– Fits very large populations
– Not accurate with small populations
Are they accurate when trying to minimize
“energy consumption”?
Deterministic Epidemic Models
• n individuals are partitioned into several
compartment
• Transition probabilities between any two
compartments are given
• The spreading of the disease is taken into consideration
C2
C1
C3
SIR
S
SI
I
Infected
Susceptibles
I
R
Recovered
s ' (t )  s (t )i (t )
i ' (t )  s (t )i (t )  i (t )
r ' (t )  i (t )
• It does not admit a generic analytic solution, but:
s(t )  s(0)e




( r ( t )  r ( 0 ))

Is the basic reproduction number:

if  >= 1/s(0) then Epidemic outbreak
SIS
SI
S
Susceptibles
I
I
Infected
i ' (t )  s (t )i (t )  i (t )
s ' (t )  i (t )  s (t )i (t )
• Solution:
i (t )  
(   )
e t (   )  c (   )  
• Using i(t) it is possible to predict the number of sick
individuals at time t
Modeling the Information Spread
• n sensors, 1 sink, 1 attacker
• A secure routing protocol allows to exchange information
between any pair of sensor
• Evolution time partitioned in rounds
– Both sensors and the attackers play their game
s(t ) is t hefract ionof sensors t hatdo not possess t hedat um
i (t ) is t hefract ionof sensorspossesingit
r (t ) is t hefract ionof sensorsdest royedby t heat t acker
Sensors Model
• Data is transmitted by replication:
– Each sensor that stores the datum transmits it with
probability  to each neighbor
n
• Theorem:
If i is the fraction of sensors possessing the datum, and if each sensor
forwards the datum with probability α/n , the value siα is an
approximation of the probability that the datum reaches a sensor that do
not possess it.
Proof
Probability that no sensors
sent the datum to Na
in





s 1  1   


n




Sensors that currently
possess the datum

siα
Probability that Na
did not possess the datum
Probability that at least one sensor
sent the datum to Na
α/n is close to 0 -> using the binomial approximation the above formula is equal to αsi
Attacker Model
• We consider 2 attackers:
– ADVsimple:
• It is able to destroy each sensors containing the datum with
probability β in each time step
– ADVstealth:
• It is able to erase the datum without destroying the sensor
• It does not change the behavior of the sensor
Epidemic models in UWSNs
ADVsimple
Replication
α/n
SIR
ADVstealth
Replication
α/n
SIS
SIR Test
•
•
•
•
α=0.605
β=0.5
n=100
i(0)=0.1
SIS Test
• n=100
• i(0)=0.1
Outcome
• Epidemic models can be used to forecast
the behavior of an UWSNs
• It becomes easy to set-up the parameters
– It is possible to study the conditions that have to be
satisfied to assure information survivability
• Problems?
– Energy Consumption: it is needed to minimize the
replication process
Minimizing Energy Consumption
• In both the models energy consumption is
minimized when i(t) is close to 0 for any t
• Statistical fluctuation can force the system to
loose the datum
n=100; i(0)=0.05
n=100; i(0)=0.01
Video Simulation SIS
n=100; α=0.22; β=0.2
Steady state when i(t)=(1-β/α)
Is the information survivability assured?
Conclusions
• Deterministic epidemic models can be used
to model information assurance in UWSNs
– The parameters that assure the survivability are easy
to set up
– They fit very well large sensor networks
• Unlikely events can induce the loss of the
datum
– It is needed to assess bounds on the probability of
these events
Questions?
Thank you!
Some Related Work
• R. Di Pietro, and N. V. Verde. Epidemic data survivability in Unattended
Wireless Sensor Networks. In Proceedings of the ACM Conference on Wireless
Network Security (WiSec), Hamburg, Germany, June 2011.
• Michele Albano, Stefano Chessa, and Roberto Di Pietro. “A model with
applications for data survivability in Critical Infrastructures”. In Journal of
Information Assurance and Security, vol. 4(6), pages 629-639, June 2009.
• Roberto Di Pietro, Luigi V. Mancini, Claudio Soriente, Angelo Spognardi, and
Gene Tsudik. “Catch Me (If You Can): Data Survival in Unattended Sensor
Networks”. In Proceedings of the 6th IEEE International Conference on Pervasive
Computing and Communications (PerCom 2008), pages 185-194, Hong Kong,
March 17-21, 2008.
• Roberto Di Pietro, Luigi V. Mancini, Claudio Soriente, Angelo Spognardi, and
Gene Tsudik. “Playing Hide-and-Seek with a Focused Mobile Adversary in
Unattended Wireless Sensor Networks”. In Journal of Ad Hoc
Networks (Elsevier) - Special Issue on Privacy and Security in Wireless Sensor
and Ad Hoc Networks -, vol. 7(8), pages 1463-1475, November 2009.