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)
Mathematical models on computer viruses. (English) Zbl 1120.68041
Summary: An attempt has been made to develop mathematical models on computer viruses infecting the system under different conditions. Mathematical model 1 discusses the situation to find the probability that at any time $t$ how many software components are infected by virus, assuming the recovery rate and proportion of un-infected population receiving infection per unit time does not change with time. Mathematical model 2 is to estimate the proportion of software component population infected at any time and at any indefinite time under different cases. The third model is to find out the rate of change of proportion of total population with exactly $j$ viruses $(1 \leqslant j < \infty )$ and proportion of total population with zero virus, assuming that the total population is distributed into different groups based on the number of viruses present in a particular module. The fourth model is to find out what is the probability that at any time $t, z$ number of software components are infected, assuming that initially (i.e. at $t = 0$), a number of components are infected and also there is a change from infected to uninfected or vice versa.

68N30Mathematical aspects of software engineering
Full Text: DOI
[1] Makinen, E.: Comment on a framework for modelling trojans and computer virus infection. Computer journal 44, 321-323 (2001) · Zbl 1051.68539
[2] F. Cohen, Computer viruses -- theory and experiments, in: DOD/NBS 7th Conference on Computer Security, originally appearing in IFIP-sec 84, also appearing in Computers and Security, vol. 6, 1987, pp. 22 -- 35.
[3] Timbley, Harlod; Anderson, Stuart; Cains, Paul: A framework for modelling trojans and computer virus infection. The computer journal 41, No. 7, 445-458 (1998)
[4] Balthrop, J.; Forrest, S.; Newman, M. E. J.; Williamson, M. M.: Technological networks and the spread of computer viruses. Science 304, No. 5670, 527-529 (2004)
[5] Aron, J. L.; Leary, M. O.; Gove, R. A.; Azadegan, S.; Schneider, M. C.: The benefits of a notification process in addressing the worsening computer virus problem: results of a survey and simulation model. Computer and security 21, 142-163 (2002)
[6] J.O. Kephart, S.R. White, Measuring and modelling computer virus prevalence, in: Proceeding of the 1993 IEEE Computer Society Symposium on Research in Security and Privacy, Oakland, California, 1993, May 24 -- 25, pp. 2 -- 14.
[7] Billings, L.; Spears, W. M.; Schwartz, I. B.: A unified prediction of computer virus spread in connected networks. Physics letters A 297, 261-266 (2002) · Zbl 0995.68007
[8] Newman, M.; Forrest, S.; Balthrop, J.: Email networks and the spread of computer viruses. Physical review E 66, 035101 (2002)
[9] Baily, N. J. T.: The mathematical theory of infectious diseases and its application. (1975)
[10] Capasoo, V.: Mathematical structure of epidemic systems. (1993)