# An Epidemic Model of Mobile Phone Virus

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4 Ralationship between coveage adius and Density=.5 coveage adius Figue 4. Ralationship between coveage adius and 4.3. Influence of moving velocity to vius Assuming distibution density of mobile phone is.35, the ange of moving velocity is m/s~3m/s, figue 5 is the elationship between moving velocity and, it pesents the influence of moving velocity to the of mobile phone vius. Fo the small distibution density of mobile phone and typical coveage adius, speeding the moving velocity can esult in the of the vius which can t spead befoe. Ralationship between moving velocity and infenction Density= moving velocity 6. Figue 5. Relationship between moving velocity and Figue 6 is the elationship between moving velocity and. It pesents the influence of moving velocity to velocity. Fom this figue we can see that inceasing of moving velocity can speed up the of vius. Relationship between moving velocity and Density= moving velocity Figue 6. Relationship between moving velocity and The time that vius file tansfes fom one mobile phone to anothe is T, the discussion above supposes f that the moving of mobile phone has no influence to vius. If we take into account the influence of moving velocity of mobile phone, we can add one subject condition: v <. When this condition is T f satisfied, vius can spead. When this condition is not satisfied, that is to say, mobile phone moves too fast, then the time that vius stay in the coveage aea of signal is too shot, vius can t spead. 5. Results of compaison with epidemic models of wom The coesponding epidemic model of wom in compute netwok can be expessed as [3]: = I ( Ω ρ I) I In compute netwok, Ω ρ is the sum of compute and it is a fixed value in shot time. The theshold of its is: < Ω ρ. If this condition is satisfied, wom can spead. This condition can be satisfied easily. Diffeent fom the theshold of compute vius, the theshold of mobile phone vius is subject to coveage adius of wieless signal, moving velocity and distibution density. Accoding to the stabilized solution of diffeential equation, we can see: if a <, then I ; fo a = ( π + v) ρ, we can get a new theshold: < ( π + v) ρ. When this condition is satisfied, vius will beak out; if this condition is not satisfied, vius can t beak out. 4

5 Fom these we can see: the condition that mobile phone vius beaks out is much moe igoous than wom in compute netwok. So the pobability of that mobile phone vius beaks out in lage aea is vey small, but it is possible in local aea. 6. Conclusions Because of the mobility, mobile phone has some elevant chaacteistics: moving velocity, moving scope etc, which make the epidemic model of mobile phone vius vey diffeent fom the model of compute vius and wom. We can make use of stochastic mobile model (such as Random Waypoint model, Random Diection model [4]) to build model of mobile phone vius. But these stochastic models have some limitations and can t accod with the fact pefeably. Fo simplification of this poblem, we build this model with unifom motion. Though the analysis of this model, we can conclude some measues of quaantining mobile phone vius: educing coveage adius, such as educing signal powe, o intefeing signal etc; deceasing moving velocity, such as esticting the flowage of peson; lessening distibution density of mobile phone, such as contolling the moving aea of someone with mobile phone; these measues have distinct diffeences with the usual ways of quaantining mobile phone vius. [6] Robet G. Cole, Nam Phamdo, Moheeb A. Rajab, Andeas Tezis. Requiements on Wom Mitigation Technologies in MANETs. Poceedings of the Wokshop on Pinciples of Advanced and Distibuted Simulation (PADS 5). [7] Shi-an Wang. Pinciple and Defense of Mobile Phone Vius. Jounal of Dal ian Institute of Light Industy, 3(): 74-76, 4. (in Chinese) [8] Kai Li, Hao Chen. Vius Theats to GSM Mobile Phones. China Infomation Secuity, 7:6-8, 5. (in Chinese) [9] Mikko Hypponen, Jano Niemela. F-Secue Vius Desciptions Commwaio. A. Mach 7 th, 5. [] Viuslist-Backdoo. WinCE.Bado, a Viuslist. Aug 5 th, 4. com/en/viuslist.html?id=98455 [] Dan Ilet and Matt Hines. Skulls pogam caies Cabi wom into phones. Techepublic. Nov 3 th, 4. /5-_-5474.html [] Sang ho Kim, Choon Seong Leem. Secuity Theats and Thei Countemeasues of Mobile Potable Computing Devices in Ubiquitous Computing Envionments. ICCSA 5, LNCS 3483, pp , 5. [3] J. Kephat and S. White. Diected-gaph epidemiological models of compute viuses. In Poceedings of the IEEE Compute Symposium on Reseach in Secuity and Pivacy, pages , May 99. [4] Bettstette, H. Hatenstein, and X. Peez-Costa. Stochastic Popeties of the Random Waypoint Mobility Model. ACM/ Kluwe Wieless Netwoks, (5): , Septembe 4. Acknowledgement This wok is suppoted in pat by National Science Foundation of China unde contact 634; by High-Tech Pogam (863) of China unde contact 3AA48. Points of view in this document ae those of the authos and do not necessaily epesent the official position of Tsinghua Univesity, Huazhong Univesity of Science and Technology, o Beijing Nomal Univesity. Refeences [] Symantec. VBS.Timofonica. html [] Symantec. SymbOS.Cabi. bos.cabi.html [3] Histoy of Compute Development. (in Chinese) [4] Neal Leavitt. Mobile Phones, The Next Fontie fo Hackes. IEEE Compute, 38(4): -3, 5. [5] James W. Mickens, Bian D. Noble. Modeling Epidemic Speading in Mobile Envionments. WiSE 5, Septembe nd, 5, Cologne, Gemany. 5

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