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In this paper, the growth of computer virus, in a given population of computers, based
on Susceptible-Infected-Susceptible (SIS) model is investigated taking into account the role
of Carriers. Three situations are considered:
Firstly, Carriers remain constant and they only spread the virus.
Secondly, Carriers remain constant and the virus is spread due to
infectives and Carriers. Thirdly, the number of Carriers decreases with time. In all the three
cases,
the asymptotic behavior of the number of infected computers with respect to time
is investigated. In this analysis, the important parameters
are: population size, epidemic threshold, birth and death rates of virus and the number of Carriers. In the first two
cases, the growth/fall of the number of infected computers asymptotically reaches a saturation value
and remains constant for large values of time. In the third
case, the same increases and reaches a maximum value and then asymptotically falls to zero.
Computer virus is one of the frontline areas
for research in the present day scenario of computer technology. This has a number of similarities with the
`biological virus'. Biological organisms and computer networks share many characteristics,
e.g., large number of connections among several simple components creating complex systems.
Computer networks can be attacked through the proliferation of a malicious
code, which spreads with virus code along the network and
produces network-wide disorders, exactly similar
to biological diseases.
Computer viruses pose a great threat to computer systems endangering both
the corporation systems of all frames and personal computers. Further, the usage of
the Internet has increased the number of damaging virus incidents. During the past few decades, the propagation of virus was taken up by
researchers with the help of a vast catalog of well-established mathematical biological
models (Kapoor, 1999) and (Murray, 2002). Out of these models, the
Susceptible-Infected-Susceptible (SIS) and
Susceptible-Infected-Removed (SIR) were commonly adopted.
In recent years, computer networks, computer automata, artificial
life, etc., have been taken up for the study of the spread and dynamics of propagation of computer virus, using
the principles of the above-mentioned models. |
