# zbMATH — the first resource for mathematics

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.

##### MSC:
 68N99 Theory of software 68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
Full Text:
##### References:
  Makinen, E., Comment on a framework for modelling trojans and computer virus infection, Computer journal, 44, 321-323, (2001) · Zbl 1051.68539  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.  Timbley, Harlod; Anderson, Stuart; Cains, Paul, A framework for modelling trojans and computer virus infection, The computer journal, 41, 7, 445-458, (1998) · Zbl 0929.68017  Balthrop, J.; Forrest, S.; Newman, M.E.J.; Williamson, M.M., Technological networks and the spread of computer viruses, Science, 304, 5670, 527-529, (2004)  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, V21, 142-163, (2002)  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.  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  Newman, M.; Forrest, S.; Balthrop, J., Email networks and the spread of computer viruses, Physical review E, 66, 035101, (2002)  Baily, N.J.T., The mathematical theory of infectious diseases and its application, (1975), Griffin London  Capasoo, V., Mathematical structure of epidemic systems, (1993), Springer Verlag
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.