This research paper describes the dynamics of propagation of computer virus in a network of computers based on the mathematical epidemiological model, Susceptible-Infected-Removed (SIR) model. The asymptotic behavior of susceptible, infected and removed nodes is examined. The threshold phenomena of growth and fall of infective nodes, based on the initial number of susceptible nodes and effective removal rate, is investigated. Further, the Kermack-McKendrick (K-M) epidemic theorem's prediction is examined under certain approximations and also a measure of intensity of the epidemic is shown.

The strong and close analogy between biological and computer viruses has compelling reasons for the adoption of the well established mathematical epidemiological models (Kapoor, 1999) in the field of computers also. These models have helped in understanding the spread of infectious diseases and the same is envisaged in the case of propagation of computer virus also. The conventional models commonly used are Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Removed (SIR) models. In this regard, extensive study has been carried out by researchers on SIS and SIR and their modified versions. These are described in the previous work of Suresh Rao et al. (2009).

Still, some crucial fundamental aspects in the basics, e.g. (1) the asymptotic behavior of susceptible, infected and removed nodes; (2) the role of removal rate; and (3) the density of susceptible nodes in the initial and final stages, need investigation. In SIS model the term epidemic threshold is used in the investigation of computer virus, whereas in SIR model, the corresponding term used is effective removal rate. This study will enable one to know about the intensity of the epidemic and the conditions under which an epidemic builds up and fades out. The density of susceptible nodes at the initial and final stage vis-à-vis the effective removal rate will throw light on the K-M threshold theorem. An emphatic study is made on these aspects in the present investigation.

Section 2 deals with the mathematical formulations. Section 3 describes the results expected from the model under different situations. The same are depicted in a graphical form. Discussions are also covered in this section.

Consider a homogeneous network of computer systems of size, N. Each computer is termed as a node. Initially, all the nodes are in good working condition, i.e., they are healthy or in other words they are termed susceptible. They are prone to infection by any external means. Any susceptible node can get infected and this infected node can further infect any other susceptible node in the system through an associated edge by which the virus propagates. The number of susceptible nodes decreases with the advancement in time and that of the infected nodes increases. Let there be another category of nodes in the network which are removed by recovery, immunization, breakdown, servicing or by any other means. The rate of infection and removal are constant in time and independent of each other and there are no fluctuations and correlations.

Computer Sciences Journal, Computer Virus, Mathematical Epidemiological Model, Susceptible-Infected-Susceptible, SIS, Mathematical Formulations, Computer Systems, Threshold Theorem, Computer Networks, Susceptible Nodes, Homogeneous Networks, Scale-free Networks.