zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Network virus-epidemic model with the point-to-group information propagation. (English) Zbl 1162.68404
Summary: Epidemiology is one of the major issues in studying the spread of computer network viruses. In this paper, a new network virus-epidemic model, namely e-SEIR, is discussed. Unlike other existing computer virus propagation models, e-SEIR takes three important network environment factors into consideration, they are (1) multi-state antivirus, (2) latent period before the infected host becomes infectious and (3) point-to-group information propagation mode. Furthermore, several related dynamics properties are investigated, along with the analysis of how to control the network computer virus prevalence based on the equilibrium stability. The simulation results show that the proposed model can serve as a basis for understanding and simulating virus epidemics in network.

Full Text: DOI
[1] Anderson, R. M.; May, R. M.: Infectious diseases of humans: dynamics and control. (1992)
[2] Britton, Nicholas F.: Essential mathematical biology. (2003)
[3] Zou, C. C.; Gong, W.; Towsley, D.: Worm propagation modeling and analysis under dynamic quarantine defense. Proceedings of the ACM CCS workshop on rapid malcode, 51-60 (2003)
[4] Chen, T.; Jamil, N.: Effectiveness of quarantine in worm epidemics. IEEE international conference on communications 2006, 2142-2147 (2006)
[5] Datta, S.; Wang, H.: The effectiveness of vaccinations on the spread of email-borne computer viruses. Ieee ccece/ccgei, 219-223 (2005)
[6] Hethcote, H. W.; Den Driessche, P. Van: Some epidemiological models with nonlinear incidence. Journal of mathematical biology 29, 271-287 (1991) · Zbl 0722.92015
[7] Keeling, M. J.; Eames, K. T. D.: Networks and epidemic models. Journal of the royal society interface 2, No. 4, 295-307 (2005)
[8] Kephart, J. O.; White, S. R.; Chess, D. M.: Computers and epidemiology. IEEE spectrum 30, 20-26 (1993)
[9] J.O. Kephart, S.R. White, Directed-graph epidemiological models of computer viruses, in: IEEE Symposium on Security and Privacy, 1991, pp. 343 -- 361.
[10] Kephart, J. O.; White, S. R.: Measuring and modeling computer virus prevalence. IEEE computer security symposium on research in security and privacy, 2-15 (1993)
[11] Korobeinikov, Andrei: Global properties of infectious disease models with nonlinear incidence. Bulletin of mathematical biology 69, 1871-1886 (2007) · Zbl 1298.92101
[12] Kuperman, M.; Abramson, G.: Small world effect in an epidemiological model. Physical review letters 86, No. 13, 2909-2912 (2001)
[13] Li, M. Y.; Muldowney, James S.; Den Driessche, P. Van: Global stability of SEIRS models in epidemiology. Canadian applied mathematics quarterly 7, No. 4, 409-425 (1999) · Zbl 0976.92020
[14] Madar, N.; Kalisky, T.; Cohen, R.; Ben Avraham, D.; Havlin, S.: Immunization and epidemic dynamics in complex networks. European physical journal B 38, 269-276 (2004)
[15] May, R. M.; Lloyd, A. L.: Infection dynamics on scale-free networks. Physical review E 64, No. 066112, 1-3 (2001)
[16] Merkin, D. R.; Rakhmilevich, D.: Introduction to the theory of stability. (1997)
[17] Liu, Wei Min; Levin, Simon A.; Iwasa, Yoh: Influence of nonlinear incidence rates upon the behavior of sirs epidemiological models. Journal of mathematical biology 23, 187-204 (1986) · Zbl 0582.92023
[18] Mishra, Bimal Kumar; Jha, Navnit: Fixed period of temporary immunity after run of anti-malicious software on computer nodes. Applied mathematics and computation 190, No. 2, 1207-1212 (2007) · Zbl 1117.92052
[19] Mishra, Bimal Kumar; Saini, Dinesh Kumar: SEIRS epidemic model with delay for transmission of malicious objects in computer network. Applied mathematics and computation 188, No. 2, 1476-1482 (2007) · Zbl 1118.68014
[20] Moore, D.; Shannon, C.; Voelker, G. M.; Savage, S.: Internet quarantine: requirements for containing self-propagating code. Proceedings of IEEE INFOCOM2003 (2003)
[21] Pastor-Satorras, R.; Vespignani, A.: Epidemics and immunization in scale-free networks. (2002)
[22] Piqueira, J. R. C.; Navarro, B. F.; Monteiro, L. H. A.: Epidemiological models applied to viruses in computer networks. Journal of computer science 1, No. 1, 31-34 (2005)
[23] Robinson, R. C.: An introduction to dynamical system: continuous and discrete. (2004) · Zbl 1073.37001
[24] Sun, Chengjun; Lin, Yiping; Tang, Shoupeng: Global stability for an special SEIR epidemic model with nonlinear incidence rates. Chaos solitons and fractals 33, 290-297 (2007) · Zbl 1152.34357
[25] Wang, Y.; Wang, C. X.: Modeling the effects of timing parameters on virus propagation. The 2003 ACM workshop on rapid malcode, 61-66 (2003)
[26] Ma.M. Williamson, J. Leill, An epidemiological model of virus spread and cleanup, 2003. <http://www.hpl.hp.com/techreports/>.
[27] Xu, Wenxiong; Zhang, Zhonghua: Global stability of SIR epidemiological model with vaccinal immunity and bilinear incidence rate. College mathematics 19, No. 6, 76-80 (2003)
[28] Zou, C. C.; Gong, W. B.; Towsley, D.; Gao, L. X.: The monitoring and early detection of Internet worms. IEEE/ACM transactions on networking 13, No. 5, 961-974 (2005)