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1- Introduction

A fascination with the potential ability of computer programs to mimic biological processes such as self-replication and the workings of the human brain dates from the earliest days of computer science  tex2html_wrap_inline1216 . Until recently, much of the work in this field (with the notable exception of genetic algorithms  tex2html_wrap_inline1218 ) was relegated to sporadic reporting in the Mathematical Games department in Scientific American. In the last few years, however, a remarkable resurgence of interest in the analogies between biological and computational mechanisms has revitalized a number of long-neglected fields, including neural networks  tex2html_wrap_inline1220 , cellular automata  tex2html_wrap_inline1222 , and artificial life  tex2html_wrap_inline1224 . Recently, a new concept has added itself to this intellectual milieu: the computer virus  tex2html_wrap_inline1226 -- a self-replicating program that spreads within computing systems, either by attaching itself parasitically to existing programs or by spawning self-sufficient copies of itself gif. The compelling analogies that exist between computer viruses and their biological counterparts have been apparent ever since the term was coined  tex2html_wrap_inline1228 . This has led some authors to suggest that the mathematical techniques which have been developed for the study of the spread of infectious diseases might be adapted to the study of the spread of computer viruses  tex2html_wrap_inline1230 . We believe that this paper represents the first serious attempt to adapt mathematical epidemiology to this problem.

In the remainder of this section, we give a very brief history of the problem of computer viruses and describe our objectives in studying them. Then, we critique some previous work on the spread of computer viruses, following it with a similar discussion of the relevant literature on mathematical epidemiology gif. We conclude that the standard epidemiological approach has much to offer, but that it must be augmented in order to account properly for the localized nature of program sharing (one of the major vectors for viral infection). Finally, we propose a model which explicitly incorporates such locality, discuss our approach to studying the behavior of that model, and provide an outline for the remainder of the paper.




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