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Speed of computer virus infection

A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?

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Hello and thank you for posting your question to Brainmass.

There are two ways to look at the problem. Each way leads to a different solution. I suspect you are looking for the firs solution. However I thought it would be useful to show you both.

Solution #1 - The discrete propagation:

We asume that the infection is done in time steps. That is at t=0 there is one infected machine, and only at t=5 we have additional 20 infected machines.

Let n be the 5 minutes step (t=5n).

After 5 minutes (n=1) we have 20+1 computers infected.

Then, after another 5 minutes (n=2) each of these computers infect 20 more, so together we have the (20+1) originals plus 20*(20+1) new ...

Solution Summary

The solution shows how to estimate the infection rate of computers by a virus if the infection is done in (a) discrete steps or (b) continuous spread.